Original: Reincarnating Reinforcement Learning: Reusing Prior Computation to Accelerate Progress
Revised: Reincarnating Reinforcement Learning: Reusing Prior Computation to Accelerate Progress

Original: Abstract
Revised: Abstract

Original: Learning tabula rasa , that is without any previously learned knowledge, is the prevalent workﬂow in reinforcement learning (RL) research.
Revised: Learning tabula rasa , that is without any previously learned knowledge, is the prevalent workﬂow in reinforcement learning (RL) research.

Original: However, RL systems, when applied to large-scale settings, rarely operate tabula rasa.
Revised: However, RL systems, when applied to large-scale settings, rarely operate tabula rasa.

Original: Such large-scale systems undergo multiple design or algorithmic changes during their development cycle and use ad hoc approaches for incorporating these changes without re-training from scratch, which would have been prohibitively expensive.
Revised: Such large-scale systems undergo multiple design or algorithmic changes during their development cycle and use ad hoc approaches for incorporating these changes without re-training from scratch, which would have been prohibitively expensive.

Original: Additionally, the inefﬁciency of deep RL typically excludes researchers without access to industrialscale resources from tackling computationally-demanding problems.
Revised: Additionally, the inefﬁciency of deep RL typically excludes researchers without access to industrialscale resources from tackling computationally-demanding problems.

Original: To address these issues, we present reincarnating RL as an alternative workﬂow or class of problem settings, where prior computational work ( e.g., learned policies) is reused or transferred between design iterations of an RL agent, or from one RL agent to another.
Revised: To address these issues, we present reincarnating RL as an alternative workﬂow or class of problem settings, where prior computational work ( e.g., learned policies) is reused or transferred between design iterations of an RL agent, or from one RL agent to another.

Original: As a step towards enabling reincarnating RL from any agent to any other agent, we focus on the speciﬁc setting of efﬁciently transferring an existing sub-optimal policy to a standalone value-based RL agent.
Revised: As a step towards enabling reincarnating RL from any agent to any other agent, we focus on the speciﬁc setting of efﬁciently transferring an existing sub-optimal policy to a standalone value-based RL agent.

Original: We ﬁnd that existing approaches fail in this setting and propose a simple algorithm to address their limitations.
Revised: We ﬁnd that existing approaches fail in this setting and propose a simple algorithm to address their limitations.

Original: Equipped with this algorithm, we demonstrate reincarnating RL’s gains over tabula rasa RL on Atari 2600 games, a challenging locomotion task, and the real-world problem of navigating stratospheric balloons.
Revised: Equipped with this algorithm, we demonstrate reincarnating RL’s gains over tabula rasa RL on Atari 2600 games, a challenging locomotion task, and the real-world problem of navigating stratospheric balloons.

Original: Overall, this work argues for an alternative approach to RL research, which we believe could signiﬁcantly improve real-world RL adoption and help democratize it further.
Revised: Overall, this work argues for an alternative approach to RL research, which we believe could signiﬁcantly improve real-world RL adoption and help democratize it further.

Original: Open-sourced code and trained agents at agarwl.github.io/reincarnating_rl .
Revised: Open-sourced code and trained agents at agarwl.github.io/reincarnating_rl .

Original:  Introduction
Revised:  Introduction

Original: Reinforcement learning (RL) is a general-purpose paradigm for making data-driven decisions.
Revised: Reinforcement learning (RL) is a general-purpose paradigm for making data-driven decisions.

Original: Due to this generality, the prevailing trend in RL research is to learn systems that can operate efﬁciently tabula rasa , that is without much learned knowledge including prior computational work such as existing datasets or learned policies.
Revised: Due to this generality, the prevailing trend in RL research is to learn systems that can operate efﬁciently tabula rasa , that is without much learned knowledge including prior computational work such as ofﬂine datasets or learned policies.

Original: However, by throwing away prior computation, tabula rasa

Original: RL impedes the ability of deep neural networks to act as a “knowledge” sponge, which is one of the reasons behind their remarkable success.

Original: Furthermore, tabula rasa RL systems are typically the exception rather than the norm for solving large-scale RL problems [3, 4, 13, 55, 75, 85].
Revised: However, tabula rasa RL systems are typically the exception rather than the norm for solving large-scale RL problems [4, 13, 55, 75, 85].

Original: Such large-scale RL systems often need to function for long periods of time and continually experience new data; restarting them from scratch may require weeks if not months of computation, and there may be billions of data points to re-process – this makes the tabula rasa approach impractical.
Revised: Such large-scale RL systems often need to function for long periods of time and continually experience new data; restarting them from scratch may require weeks if not months of computation, and there may be billions of data points to re-process – this makes the tabula rasa approach impractical.

Original: For example, the system that plays Dota 2 at a human-like level [13] underwent several months of RL training with continual changes ( e.g., in model architecture, environment, etc ) during its development; this necessitated building upon the previously trained system after such changes to circumvent retraining from scratch, which was done using ad hoc approaches.
Revised: For example, the system that plays Dota 2 at a human-like level [13] underwent several months of RL training with continual changes ( e.g., in model architecture, environment, etc ) during its development; this necessitated building upon the previously trained system after such changes to circumvent re-training from scratch, which was done using ad hoc approaches (described in Section 3).

Revised: Current RL research also excludes the majority of researchers outside certain resource-rich labs from tackling complex problems, as doing so often incurs substantial computational and ﬁnancial cost:

Original: Furthermore, tackling challenging problems with deep RL often incurs substantial computational and ﬁnancial cost: AlphaStar [85], which achieves grandmaster level in StarCraft, was trained using TPUs for more than a month and replicating it would cost several million dollars (Appendix A.1). 
Revised: AlphaStar [85], which achieves grandmaster level in StarCraft, was trained using TPUs for more than a month and replicating it would cost several million dollars (Appendix A.1). Even the quintessential deep RL benchmark of training an agent on 50+ Atari games [10], with at least 5 runs, requires more than 1000 GPU days.

Original: As a result, the majority of the  RL community outside certain resource-rich labs is currently excluded from tackling such problems.
Revised: As deep RL research move towards more challenging problems, the computational barrier to entry in RL research is likely to further increase.

Original: To address both the computational and sample inefﬁciencies of tabula rasa RL we present reincarnating RL (RRL) as an alternative research workﬂow or a class of problems to focus on.
Revised: To address both the computational and sample inefﬁciencies of tabula rasa RL we present reincarnating RL (RRL) as an alternative research workﬂow or a class of problems to focus on.

Original: RRL seeks to maximally leverage existing computational work, such as learned network weights and collected data , to accelerate training across design iterations of an RL agent or when moving from one agent to another.
Revised: RRL seeks to maximally leverage existing computational work, such as learned network weights and collected data , to accelerate training across design iterations of an RL agent or when moving from one agent to another.

Original: In RRL, agents need not be trained tabula rasa, except for initial forays into new problems.
Revised: In RRL, agents need not be trained tabula rasa, except for initial forays into new problems.

Original: For example, imagine a researcher who has trained an agent A 1 for a long time ( e.g., weeks) but now this or another researcher wants to experiment with better architectures or RL algorithms.
Revised: For example, imagine a researcher who has trained an agent A 1 for a long time ( e.g., weeks), but now this or another researcher wants to experiment with better architectures or RL algorithms.

Original: While the tabula rasa workﬂow requires re-training another agent from scratch, reincarnating RL provides the more viable option of transferring A 1 to another agent and training this agent further, or simply ﬁne-tuning A 1 (Figure 1).
Revised: While the tabula rasa workﬂow requires re-training another agent from scratch, reincarnating RL provides the more viable option of transferring A 1 to another agent and training this agent further, or simply ﬁne-tuning A 1 (Figure 1).

Original: As such, RRL can be viewed as an attempt to provide a formal foundation for the research workﬂow needed for real-world and large-scale RL models.
Revised: As such, RRL can be viewed as an attempt to provide a formal foundation for the research workﬂow needed for real-world and large-scale RL models.

Original: Reincarnating RL can democratize research by allowing the broader community to tackle larger-scale and complex RL problems without requiring excessive computational resources.
Revised: Reincarnating RL can democratize research by allowing the broader community to tackle larger-scale and complex RL problems without requiring excessive computational resources.

Original: As a consequence,
Revised: As a consequence,

Original: RRL can also help avoid the risk of researchers overﬁtting to conclusions from small-scale RL problems.
Revised: RRL can also help avoid the risk of researchers overﬁtting to conclusions from small-scale RL problems.

Original: Furthermore, RRL can enable a benchmarking paradigm where researchers continually improve and update existing trained agents, especially on problems where improving performance has real-world impact ( e.g., balloon navigation [11], chip design [59], tokamak control [24]).
Revised: Furthermore, RRL can enable a benchmarking paradigm where researchers continually improve and update existing trained agents, especially on problems where improving performance has real-world impact ( e.g., balloon navigation [11], chip design [59], tokamak control [24]).

Original: Furthermore, a common real-world RL use case will likely be in scenarios where prior computational work is available ( e.g., existing deployed RL policies), making RRL important to study.
Revised: Furthermore, a common real-world RL use case will likely be in scenarios where prior computational work is available ( e.g., existing deployed RL policies), making RRL important to study.

Original: However, beyond some ad hoc large-scale reincarnation efforts (Section 3), the community has not focused much on studying reincarnating RL as a research problem in its own right.
Revised: However, beyond some ad hoc large-scale reincarnation efforts (Section 3), the community has not focused much on studying reincarnating RL as a research problem in its own right.

Original: To this end, this work argues for developing general-purpose RRL approaches as opposed to ad hoc solutions.
Revised: To this end, this work argues for developing general-purpose RRL approaches as opposed to ad hoc solutions.

Original: Different RRL problems can be instantiated depending on how the prior computational work is provided: logged datasets, learned policies, pretrained models, representations, etc .
Revised: Different RRL problems can be instantiated depending on how the prior computational work is provided: logged datasets, learned policies, pretrained models, representations, etc .

Original: As a step towards developing broadly applicable reincarnation approaches, we focus on the speciﬁc setting of policy-to-value reincarnating RL (PVRL) for efﬁciently transferring a suboptimal teacher policy to a value-based RL student agent (Section 4).
Revised: As a step towards developing broadly applicable reincarnation approaches, we focus on the speciﬁc setting of policy-to-value reincarnating RL (PVRL) for efﬁciently transferring a suboptimal teacher policy to a value-based RL student agent (Section 4).

Original: Since it is undesirable to maintain dependency on past teachers for successive reincarnations, we require a PVRL algorithm to “wean” off the teacher dependence as training progresses.
Revised: Since it is undesirable to maintain dependency on past teachers for successive reincarnations, we require a PVRL algorithm to “wean” off the teacher dependence as training progresses.

Original: We ﬁnd that prior approaches, when evaluated for PVRL on the Arcade Learning Environment (ALE) [10], either result in small improvements over the tabula rasa student or exhibit degradation when weaning off the teacher.
Revised: We ﬁnd that prior approaches, when evaluated for PVRL on the Arcade Learning Environment (ALE) [10], either result in small improvements over the tabula rasa student or exhibit degradation when weaning off the teacher.

Original: To address these limitations, we introduce QDagger, which combines Dagger [71] with n -step Q-learning, and outperforms prior approaches.
Revised: To address these limitations, we introduce QDagger, which combines Dagger [71] with n -step Q-learning, and outperforms prior approaches.

Original: Equipped with QDagger, we demonstrate the sample and compute-efﬁciency gains of reincarnating RL over tabula rasa RL, on ALE, a humanoid locomotion task and the simulated real-world problem of navigating stratospheric balloons [11] (Section 5).
Revised: Equipped with QDagger, we demonstrate the sample and compute-efﬁciency gains of reincarnating RL over tabula rasa RL, on ALE, a humanoid locomotion task and the simulated real-world problem of navigating stratospheric balloons [11] (Section 5).

Original: Finally, we discuss some considerations in RRL as well as address reproducibility and generalizability concerns.
Revised: Finally, we discuss some considerations in RRL as well as address reproducibility and generalizability concerns.

Original:  Preliminaries
Revised:  Preliminaries

Original: The goal in RL is to maximize the long-term discounted reward in an environment.
Revised: The goal in RL is to maximize the long-term discounted reward in an environment.

Original: We model the environment as an MDP, deﬁned as ( S , A , R, P, γ ) [69], with a state space S , an action space A , a stochastic reward function R ( s, a ) , transition dynamics P ( s (cid:48) | s, a ) and a discount factor γ ∈ [0 , 1) .
Revised: We model the environment as an MDP, deﬁned as ( S , A , R, P, γ ) [69], with a state space S , an action space A , a stochastic reward function R ( s, a ) , transition dynamics P ( s (cid:48) | s, a ) and a discount factor γ ∈ [0 , 1) .

Original: A policy π ( ·| s ) maps states to a distribution over actions.
Revised: A policy π ( ·| s ) maps states to a distribution over actions.

Original: The Q-value function Q π ( s, a ) for a policy π ( ·| s ) is the expected sum of discounted rewards obtained by executing action a at state s and following π ( ·| s ) thereafter.Q π ( s, a ) is the ﬁxed point of Q ( s, a ) = R ( s, a ) + γE s (cid:48) ∼ P ( ·| s,a ) ,a (cid:48) ∼ π ( ·| s (cid:48) ) [ Q ( s (cid:48) , a (cid:48) )] .
Revised: The Q-value function Q π ( s, a ) for a policy π ( ·| s ) is the expected sum of discounted rewards obtained by executing action a at state s and following π ( ·| s ) thereafter.

Original: DQN [60] builds on Q-learning [87] and parameterizes the Qvalue function, Q θ , with a neural net with parameters θ while following an (cid:15) -greedy policy with respect to Q θ for data collection.
Revised: DQN [60] builds on Q-learning [87] and parameterizes the Q-value function, Q θ , with a neural net with parameters θ while following an (cid:15) -greedy policy with respect to Q θ for data collection.

Original: DQN minimizes the temporal difference (TD) loss, L TD ( D S ) , on transition tuples, ( s, a, r, s (cid:48) ) , sampled from an experience replay buffer D S collected during training:
Revised: DQN minimizes the temporal difference (TD) loss, L TD ( D S ) , on transition tuples, ( s, a, r, s (cid:48) ) , sampled from an experience replay buffer D S collected during training:

Original: [Equation]
Revised: [Equation]

Original:  where ¯ Q θ is a delayed copy of the same Q-network, referred to as the target network .
Revised: ¯ Q θ ( s (cid:48) , a (cid:48) ) (cid:1) 2 (cid:105) (1) where ¯ Q θ is a delayed copy of the same Q-network, referred to as the target network .

Original: Modern valuebased RL agents, such as Rainbow [35], use n -step returns to further stabilize learning.
Revised: Modern valuebased RL agents, such as Rainbow [35], use n -step returns to further stabilize learning.

Original: Speciﬁcally, rather than training the Q-value estimate Q ( s t , a t ) on the basis of the single-step temporal difference error r t + γ max a (cid:48) Q ( s t +1 , a (cid:48) )
Revised: Speciﬁcally, rather than training the Q-value estimate Q ( s t , a t ) on the basis of the single-step temporal difference error r t + γ max a (cid:48) Q ( s t +1 , a (cid:48) )

Original: − Q ( s t , a t ) , an n -step target (cid:80) n − 1 k =

Revised: − Q ( s t , a t ) , an n -step target (cid:80) n − 1 k =

Original: γ k r t + k + γ n max a (cid:48) Q ( s t + n , a (cid:48) )
Revised: γ k r t + k + γ n max a (cid:48) Q ( s t + n , a (cid:48) )

Original: −
Revised: −

Original: Q ( s t , a t ) is used in the TD loss, with intermediate future rewards stored in the replay D .
Revised: Q ( s t , a t ) is used in the TD loss, with intermediate future rewards stored in the replay D .

Original:  Related work
Revised:  Related work

Original: Prior ad hoc reincarnation efforts .
Revised: Prior ad hoc reincarnation efforts .

Original: While several high-proﬁle RL achievements have used reincarnation, it has typically been done in an ad-hoc way and has limited applicability.
Revised: While several high-proﬁle RL achievements have used reincarnation, it has typically been done in an ad-hoc way and has limited applicability.

Original: OpenAI Five [13], which can play Dota 2 at a human-like level, required 10 months of large-scale RL training and went through continual changes in code and environment ( e.g., expanding observation spaces) during development.
Revised: OpenAI Five [13], which can play Dota 2 at a human-like level, required 10 months of large-scale RL training and went through continual changes in code and environment ( e.g., expanding observation spaces) during development.

Original: To avoid restarting from scratch after such changes, OpenAI Five used “ surgery ” akin to Net2Net [17] style transformations to convert a trained model to certain bigger architectures with custom weight initializations.
Revised: To avoid restarting from scratch after such changes, OpenAI Five used “ surgery ” akin to Net2Net [17] style transformations to convert a trained model to certain bigger architectures with custom weight initializations.

Original: AlphaStar [85] employs population-based training ( PBT ) [42], which periodically copies weights of the best performing value-based agents and mutates hyperparameters during training.
Revised: AlphaStar [85] employs population-based training ( PBT ) [42], which periodically copies weights of the best performing value-based agents and mutates hyperparameters during training.

Original: Although PBT and surgery methods are efﬁcient, they have they can not be used for reincarnating RL when switching to arbitrary architectures ( e.g., feed-forward to recurrent networks) or from one model class to another ( e.g., policy to a value function).
Revised: Although PBT and surgery methods are efﬁcient, they have they can not be used for reincarnating RL when switching to arbitrary architectures ( e.g., feed-forward to recurrent networks) or from one model class to another ( e.g., policy to a value function).

Original: Akkaya et al.
Revised: Akkaya et al.

Original: [4] trained RL policies for several months to manipulate a robot hand for solving Rubik’s cube.
Revised: [4] trained RL policies for several months to manipulate a robot hand for solving Rubik’s cube.

Original: To do so, they “rarely trained experiments from scratch” but instead initialized new policies, with architectural changes, from previous trained policies using behavior cloning via on-policy distillation [20, 67].
Revised: To do so, they “rarely trained experiments from scratch” but instead initialized new policies, with architectural changes, from previous trained policies using behavior cloning via on-policy distillation [20, 67].

Original: AlphaGo [75] also used behavior cloning on human replays for initializing the policy and ﬁne-tuning it further with RL.
Revised: AlphaGo [75] also used behavior cloning on human replays for initializing the policy and ﬁne-tuning it further with RL.

Original: However, behavior cloning is only applicable for policy to policy transfer and is inadequate for the PVRL setting of transferring a policy to a value function [ e.g., 63, 83].
Revised: However, behavior cloning is only applicable for policy to policy transfer and is inadequate for the PVRL setting of transferring a policy to a value function [ e.g., 63, 83].

Original: Contrary to such approaches, we apply reincarnation in settings where these approaches are not applicable including transferring a DQN agent to Impala-CNN Rainbow in ALE, and a distributed agent with
Revised: Contrary to such approaches, we apply reincarnation in settings where these approaches are not applicable including transferring a DQN agent to Impala-CNN Rainbow in ALE, and a distributed agent with

Original: MLP architecture to a recurrent agent in BLE.
Revised: MLP architecture to a recurrent agent in BLE.

Original: Several prior works also ﬁne-tune existing agents with deep RL for reducing training time, especially on real-world tasks such as chip ﬂoor-planning [59], robotic manipulation [43], aligning language models [6], and compiler optimization [82].
Revised: Several prior works also ﬁne-tune existing agents with deep RL for reducing training time, especially on real-world tasks such as chip ﬂoor-planning [59], robotic manipulation [43], aligning language models [6], and compiler optimization [82].

Original: In line with these works, we ﬁnd that ﬁne-tuning a value-based agent can be an effective reincarnation strategy (Figure 7).
Revised: In line with these works, we ﬁnd that ﬁne-tuning a value-based agent can be an effective reincarnation strategy (Figure 7).

Original: However, ﬁne-tuning is often constrained to use the same architecture as the agent being ﬁne-tuned.
Revised: However, ﬁne-tuning is often constrained to use the same architecture as the agent being ﬁne-tuned.

Original: Instead, we focus on reincarnating RL methods that do not have this limitation.
Revised: Instead, we focus on reincarnating RL methods that do not have this limitation.

Original: Leveraging prior computation .
Revised: Leveraging prior computation .

Original: While areas such as ofﬂine RL, imitation learning, transfer in RL, continual RL etc focus on developing methods to leverage prior computation, such areas don’t strive to change how we do RL research by incorporating such methods as a part of our workﬂow.
Revised: While areas such as ofﬂine RL, imitation learning, transfer in RL, continual RL etc focus on developing methods to leverage prior computation, such areas don’t strive to change how we do RL research by incorporating such methods as a part of our workﬂow.

Original: For completeness, we contrast closely related approaches to PVRL, the RRL setting we study.
Revised: For completeness, we contrast closely related approaches to PVRL, the RRL setting we study.

Original: - Leveraging existing agents .
Revised: - Leveraging existing agents .

Original: Existing policies have been previously used for improving data collection [14, 16, 28, 77, 89]; we evaluate one such approach, JSRL [83], which improves exploration in goal-reaching RL tasks.
Revised: Existing policies have been previously used for improving data collection [14, 16, 28, 77, 89]; we evaluate one such approach, JSRL [83], which improves exploration in goal-reaching RL tasks.

Original: However, our PVRL experiments indicate that JSRL performs poorly on ALE.
Revised: However, our PVRL experiments indicate that JSRL performs poorly on ALE.

Original: Schmitt et al.
Revised: Schmitt et al.

Original: [74] propose kickstarting to speed-up actor-critic agents using an interactive teacher policy by combining on-policy distillation [20, 67] with RL.
Revised: [74] propose kickstarting to speed-up actor-critic agents using an interactive teacher policy by combining on-policy distillation [20, 67] with RL.

Original: Empirically, we ﬁnd that kickstarting is a strong baseline for PVRL, however it exhibits unstable behavior without n -step returns and underperforms QDagger.
Revised: Empirically, we ﬁnd that kickstarting is a strong baseline for PVRL, however it exhibits unstable behavior without n -step returns and underperforms QDagger.

Original: PVRL also falls under the framework of agents teaching agents (ATA) [21] with RL-based students and teachers.
Revised: PVRL also falls under the framework of agents teaching agents (ATA) [21] with RL-based students and teachers.

Original: While ATA approaches, such as action advice [81], emphasize how and when to query the teacher or evaluating the utility of teacher advice, PVRL focuses on sample-efﬁcient transfer and does not impose constraints on querying the teacher.
Revised: While ATA approaches, such as action advice [81], emphasize how and when to query the teacher or evaluating the utility of teacher advice, PVRL focuses on sample-efﬁcient transfer and does not impose constraints on querying the teacher.

Original: PVRL is also different from prior work on accelerating RL using a heuristic or oracle value function [9, 19, 78], as PVRL only assumes access to a suboptimal policy.
Revised: PVRL is also different from prior work on accelerating RL using a heuristic or oracle value function [9, 19, 78], as PVRL only assumes access to a suboptimal policy.

Original: Unlike PVRL methods that wean off the teacher, imitation-regularized RL methods [51, 61] stay close to the suboptimal teacher, which can limit the student’s performance with continued training (Figure 9).
Revised: Unlike PVRL methods that wean off the teacher, imitation-regularized RL methods [51, 61] stay close to the suboptimal teacher, which can limit the student’s performance with continued training (Figure 9).

Original: - Leveraging prior data .
Revised: - Leveraging prior data .

Original: Learning from demonstrations (LfD) [5, 30, 36, 40, 72] approaches focus on accelerating RL training using demonstrations.
Revised: Learning from demonstrations (LfD) [5, 30, 36, 40, 72] approaches focus on accelerating RL training using demonstrations.

Original: Such approaches typically assume access to optimal or near-optimal trajectories, often obtained from human demonstrators, and aim to match the demonstrator’s performance.
Revised: Such approaches typically assume access to optimal or near-optimal trajectories, often obtained from human demonstrators, and aim to match the demonstrator’s performance.

Original: Instead, PVRL focuses on leveraging a suboptimal teacher policy, which can be obtained from any trained RL agent, that we wean off during training.
Revised: Instead, PVRL focuses on leveraging a suboptimal teacher policy, which can be obtained from any trained RL agent, that we wean off during training.

Original: Empirically, we ﬁnd that DQfD [36], a well-known LfD approach to accelerate deep Q-learning, when applied to PVRL, exhibits severe performance degradation when weaning off the teacher.
Revised: Empirically, we ﬁnd that DQfD [36], a well-known LfD approach to accelerate deep Q-learning, when applied to PVRL, exhibits severe performance degradation when weaning off the teacher.

Original: Rehearsal approaches [62, 66, 76] focus on improving exploration by replaying demonstrations during learning; we ﬁnd that such approaches are ineffective for leveraging the teacher in PVRL.
Revised: Rehearsal approaches [62, 66, 76] focus on improving exploration by replaying demonstrations during learning; we ﬁnd that such approaches are ineffective for leveraging the teacher in PVRL.

Original: Ofﬂine RL [1, 49, 52] focuses on learning solely from ﬁxed datasets while reincarnating RL focuses on leveraging prior information, which can also be presented as ofﬂine datasets, for speeding up further learning from environment interactions.
Revised: Ofﬂine RL [1, 49, 52] focuses on learning solely from ﬁxed datasets while reincarnating RL focuses on leveraging prior information, which can also be presented as ofﬂine datasets, for speeding up further learning from environment interactions.

Original: Recent work [45, 51, 55, 63] use ofﬂine RL to pretrain on prior data and then ﬁne-tune online.
Revised: Recent work [45, 51, 55, 63] use ofﬂine RL to pretrain on prior data and then ﬁne-tune online.

Original: We also evaluate this pretraining approach for PVRL and ﬁnd that it underperforms QDagger, which utilizes the interactive teacher policy in addition to the prior teacher collected data.
Revised: We also evaluate this pretraining approach for PVRL and ﬁnd that it underperforms QDagger, which utilizes the interactive teacher policy in addition to the prior teacher collected data.

Original:  Case Study: Policy to Value Reincarnating RL
Revised:  Case Study: Policy to Value Reincarnating RL

Original: While prior large-scale efforts have used a limited form of reincarnating RL (Section 3), it is unclear how to design more broadly applicable RRL approaches.
Revised: While prior large-scale efforts have used a limited form of reincarnating RL (Section 3), it is unclear how to design more broadly applicable RRL approaches.

Original: To exemplify the challenges of designing such approaches, we focus on the RRL setting for accelerating training of a student agent given access to a suboptimal teacher policy and some data from it.
Revised: To exemplify the challenges of designing such approaches, we focus on the RRL setting for accelerating training of a student agent given access to a suboptimal teacher policy and some data from it.

Original: While a policy-based student can be easily reincarnated in this setting via behavior cloning [ e.g., 4], we study the more challenging policy-to-value reincarnating RL ( PVRL ) setting for transferring a policy to a value-based student agent.
Revised: While a policy-based student can be easily reincarnated in this setting via behavior cloning [ e.g., 4], we study the more challenging policy-to-value reincarnating RL ( PVRL ) setting for transferring a policy to a value-based student agent.

Original: While we can obtain a policy from any RL agent, we chose this setting because value-based
Revised: While we can obtain a policy from any RL agent, we chose this setting because value-based

Original: RL methods (Q-learning, actor-critic) can leverage off-policy data for better sample efﬁciency.
Revised: RL methods (Q-learning, actor-critic) can leverage off-policy data for better sample efﬁciency.

Original: To be broadly useful for reincarnating agents, a PVRL algorithm should satisfy the following desiderata:
Revised: To be broadly useful for reincarnating agents, a PVRL algorithm should satisfy the following desiderata:

Original: • Teacher-agnostic .
Revised: • Teacher-agnostic .

Original: Reincarnating RL has limited utility if the student is constrained by the teacher’s architecture or learning algorithm.
Revised: Reincarnating RL has limited utility if the student is constrained by the teacher’s architecture or learning algorithm.

Original: Thus, we require the student to be teacher-agnostic.
Revised: Thus, we require the student to be teacher-agnostic.

Original: • Weaning .
Revised: • Weaning .

Original: It is undesirable to maintain dependency on past teachers when reincarnation may occur several times over the course of a project, or one project to another.
Revised: It is undesirable to maintain dependency on past teachers when reincarnation may occur several times over the course of a project, or one project to another.

Original: Thus , it is necessary that the student’s dependence on the teacher policy can be weaned off, as training progresses.
Revised: Thus, it is necessary that the student’s dependence on the teacher policy can be weaned off, as training progresses.

Original: • Sample-efﬁcient .
Revised: • Compute & sample efﬁcient .

Original: Naturally, reincarnating RL is only useful if it is computationally cheaper than training from scratch.
Revised: Naturally, RRL is only useful if it is computationally cheaper than training from scratch.

Original: Thus, it is desirable that the student can recover and possibly improve upon the teacher’s performance using fewer environment samples than training tabula rasa.
Revised: Thus, it is desirable that the student can recover and possibly improve upon the teacher’s performance using fewer environment samples than training tabula rasa.

Original: PVRL on Atari 2600 games .
Revised: PVRL on Atari 2600 games .

Original: Given the above desiderata for PVRL, we now empirically investigate whether existing methods that leverage existing data or agents (see Section 3) sufﬁce for PVRL.
Revised: Given the above desiderata for PVRL, we now empirically investigate whether existing methods that leverage existing data or agents (see Section 3) sufﬁce for PVRL.

Original: The speciﬁc methods that we consider were chosen because they are simple to implement, and also because they have been designed with closely related goals in mind.
Revised: The speciﬁc methods that we consider were chosen because they are simple to implement, and also because they have been designed with closely related goals in mind.

Original: Experimental setup .
Revised: Experimental setup .

Original: We conduct experiments on ALE with sticky actions [57].
Revised: We conduct experiments on ALE with sticky actions [57].

Original: To reduce the computational cost of our experiments, we use a subset of 10 commonly-used Atari 2600 games:
Revised: To reduce the computational cost of our experiments, we use a subset of 10 commonly-used Atari 2600 games:

Original: Asterix, Breakout, Space Invaders, Seaquest, Q ∗ Bert, Beam Rider, Enduro, Ms Pacman, Bowling and
Revised: Asterix, Breakout, Space Invaders, Seaquest, Q ∗ Bert, Beam Rider, Enduro, Ms Pacman, Bowling and

Original: River Raid.
Revised: River Raid.

Original: We obtain the teacher policy π T by running DQN [60] with Adam optimizer formillion environment frames, requiring 7 days of training per run with Dopamine [15] on P100 GPUs. 
Revised: We obtain the teacher policy π T by running DQN [60] with Adam optimizer formillion environment frames, requiring 7 days of training per run with Dopamine [15] on P100 GPUs. QDagger [Figure]

Original: We also assume access to a dataset D T that can be generated by the teacher (see Appendix A.5 for results about dependence on D T ).
Revised: We also assume access to a dataset D T that can be generated by the teacher (see Appendix A.5 for results about dependence on D T ).

Original: For this work, D T is the ﬁnal replay buffer (1M transitions) logged[Figure] by the teacher DQN, which is 100 times smaller than the data the teacher was trained on.
Revised: For this work, D T is the ﬁnal replay buffer (1M transitions) logged by the teacher DQN, which is 100 times smaller than the data the teacher was trained on.

Original: For a challenging PVRL setting, we use DQN as the student since tabula rasa DQN requires a substantial amount of training to reach the teacher’s performance.
Revised: For a challenging PVRL setting, we use DQN as the student since tabula rasa DQN requires a substantial amount of training to reach the teacher’s performance.

Original: To emphasize sample-efﬁcient reincarnation, we train this student for only 10 million frames, a 40 times smaller sample budget than the teacher.
Revised: To emphasize sample-efﬁcient reincarnation, we train this student for only 10 million frames, a 40 times smaller sample budget than the teacher.

Original: Furthermore, we wean off the teacher at 6 million frames.
Revised: Furthermore, we wean off the teacher at 6 million frames.

Original: See Appendix A.3 for more details.
Revised: See Appendix A.3 for more details.

Original: Evaluation .
Revised: Evaluation .

Original: For reliable evaluation, we follow the recommendations of Agarwal et al.
Revised: Following Agarwal et al.

Original: [2] and report the Interquartile Mean (IQM) normalized scores with 95%bootstrap conﬁdence intervals (CIs), aggregated across 10Atari games with 3 seeds each.
Revised: [2], we report interquartile mean normalized scores with 95% conﬁdence intervals (CIs), aggregated across 10 games with 3 seeds each.

Original: The normalization is done such that the random policy corresponds to a score of 0 and the teacher policy π T corresponds to a score of 1.
Revised: The normalization is done such that the random policy obtains a score of 0 and the teacher policy π T obtains a score of 1.

Original: This differs from typically reported human-normalized scores, as we wanted to highlight the performance differences between the student and the teacher.
Revised: This differs from typically reported human-normalized scores, as we wanted to highlight the performance differences between the student and the teacher.

Original: Next, we describe the approaches we investigate.
Revised: Next, we describe the approaches we investigate.

Original: • Rehearsal : Since the student, in principle, can learn using any off-policy data, we can replay teacher data D T along with the student’s own interactions during training.
Revised: • Rehearsal : Since the student, in principle, can learn using any off-policy data, we can replay teacher data D T along with the student’s own interactions during training.

Original: Following Paine et al.
Revised: Following Paine et al.

Original: [66], the student minimizes the TD loss on mini-batches that contain ρ % of the samples from D T and the rest from the student’s replay D S (different ρ and n -step values in Figure A.12).
Revised: [66], the student minimizes the TD loss on mini-batches that contain ρ % of the samples from D T and the rest from the student’s replay D S (different ρ and n -step values in Figure A.12).

Original: • JSRL (Figure 3, left): JSRL [83] uses an interactive teacher policy as a “guide” to improve exploration and rolls in with the guide for a random number of environment steps.
Revised: • JSRL (Figure 3, left): JSRL [83] uses an interactive teacher policy as a “guide” to improve exploration and rolls in with the guide for a random number of environment steps.

Original: To evaluate JSRL, we vary the maximum number of roll-in steps, α , that can be taken by the teacher and sample a random number of roll-in steps between [0 , α ] every episode.
Revised: To evaluate JSRL, we vary the maximum number of roll-in steps, α , that can be taken by the teacher and sample a random number of roll-in steps between [0 , α ] every episode.

Original: As the student improves, we decay the steps taken by the teacher every iteration (1M frames) by a factor of β . • Ofﬂine RL Pretraining :
Revised: As the student improves, we decay the steps taken by the teacher every iteration (1M frames) by a factor of β . • Ofﬂine RL Pretraining :

Original: Given access to teacher data D T , we can pre-train the student using ofﬂine RL.
Revised: Given access to teacher data D T , we can pre-train the student using ofﬂine RL.

Original: To do so, we use CQL [46], a widely used ofﬂine RL algorithm, which jointly minimizes the TD and behavior cloning on logged transitions in D T (Equation A.3).
Revised: To do so, we use CQL [46], a widely used ofﬂine RL algorithm, which jointly minimizes the TD and behavior cloning on logged transitions in D T (Equation A.3).

Original: Following pretraining, we ﬁne-tune the learned Q-network using TD loss on the student’s replay D S .
Revised: Following pretraining, we ﬁne-tune the learned Q-network using TD loss on the student’s replay D S .

Original: • Kickstarting (Figure 3, right):
Revised: • Kickstarting (Figure 3, right):

Original: Akin to kickstarting [74], we jointly optimize the TD loss with an on-policy distillation loss on the student’s self-collected data in D S .
Revised: Akin to kickstarting [74], we jointly optimize the TD loss with an on-policy distillation loss on the student’s self-collected data in D S .

Original: The distillation loss uses the cross-entropy between teacher’s policy π T and the student policy π ( ·| s ) =
Revised: The distillation loss uses the cross-entropy between teacher’s policy π T and the student policy π ( ·| s ) =

Original: softmax( Q ( s, · ) /τ ) , where τ corresponds to temperature.
Revised: softmax( Q ( s, · ) /τ ) , where τ corresponds to temperature.

Original: To wean off the teacher, we decay the distillation coefﬁcient as training progresses.
Revised: To wean off the teacher, we decay the distillation coefﬁcient as training progresses.

Original: Note that kickstarting does not pretrain on teacher data.
Revised: Note that kickstarting does not pretrain on teacher data.

Original: • DQfD (Figure 4, left): Following DQfD [35], we initially pretrain the student on teacher data D T using a combination of TD loss with a large margin classiﬁcation loss to imitate the teacher actions (Equation A.4).
Revised: • DQfD (Figure 4, left): Following DQfD [35], we initially pretrain the student on teacher data D T using a combination of TD loss with a large margin classiﬁcation loss to imitate the teacher actions (Equation A.4).

Original: After pretraining, we train the student on its replay data D S , again using a combination of TD and margin loss.
Revised: After pretraining, we train the student on its replay data D S , again using a combination of TD and margin loss.

Original: While DQfD minimizes the margin loss throughout training, we decay the margin loss coefﬁcient during the online phase, akin to kickstarting.
Revised: While DQfD minimizes the margin loss throughout training, we decay the margin loss coefﬁcient during the online phase, akin to kickstarting.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: Results .
Revised: Results .

Original: Rehearsal, with best-performing teacher data ratio ( ρ = 1 / 16 ), is marginally better than tabula rasa DQN but signiﬁcantly underperforms the teacher (Figure 2, teal), which seems related to the difﬁculty of standard value-based methods to learn from off-policy teacher data [65].
Revised: Rehearsal, with best-performing teacher data ratio ( ρ = 1 / 16 ), is marginally better than tabula rasa DQN but signiﬁcantly underperforms the teacher (Figure 2, teal), which seems related to the difﬁculty of standard value-based methods to learn from off-policy teacher data [65].

Original: JSRL does not improve performance compared to tabula rasa DQN and even hurts performance with a large number of teacher roll-in steps (Figure 3, left).
Revised: JSRL does not improve performance compared to tabula rasa DQN and even hurts performance with a large number of teacher roll-in steps (Figure 3, left).

Original: The ineffectiveness of JSRL on ALE is likely due to the state-distribution mismatch between the student and the teacher, as the student may never visit the states visited by the teacher and as a result, doesn’t learn to correct for its previous mistakes [16].
Revised: The ineffectiveness of JSRL on ALE is likely due to the state-distribution mismatch between the student and the teacher, as the student may never visit the states visited by the teacher and as a result, doesn’t learn to correct for its previous mistakes [16].

Original: Pretraining with ofﬂine RL on logged teacher data recovers around 50% of the teacher’s performance and ﬁne-tuning this pretrained Q-function online marginally improves performance (Figure 2, pink).
Revised: Pretraining with ofﬂine RL on logged teacher data recovers around 50% of the teacher’s performance and ﬁne-tuning this pretrained Q-function online marginally improves performance (Figure 2, pink).

Original: However, ﬁne-tuning degrades performance with 1 -step returns, which is more pronounced with higher values of CQL loss coefﬁcient (Figure A.13).
Revised: However, ﬁne-tuning degrades performance with 1 -step returns, which is more pronounced with higher values of CQL loss coefﬁcient (Figure A.13).

Original: We also ﬁnd that kickstarting exhibits performance degradation (Figure 3, right), which is severe with 1 -step returns, once we wean off the teacher policy.
Revised: We also ﬁnd that kickstarting exhibits performance degradation (Figure 3, right), which is severe with 1 -step returns, once we wean off the teacher policy.

Original: Akin to kickstarting, we again observe a severe performance collapse when weaning off the the teacher dependence in DQfD (Figure 4, left), even when using n -step returns.
Revised: Akin to kickstarting, we again observe a severe performance collapse when weaning off the the teacher dependence in DQfD (Figure 4, left), even when using n -step returns.

Original: We hypothesize that this performance degradation is caused by the inconsistency between Q-values trained using a combination of imitation learning and TD losses, as opposed to only minimizing the TD loss.
Revised: We hypothesize that this performance degradation is caused by the inconsistency between Q-values trained using a combination of imitation learning and TD losses, as opposed to only minimizing the TD loss.

Original: We also ﬁnd that using intermediate values of n -step returns, such as n = 3 (also used by Rainbow [35]), quickly recovers after the performance drop from weaning while larger n -step values impede learning, possibly due to stale target Q-values.
Revised: We also ﬁnd that using intermediate values of n -step returns, such as n = 3 (also used by Rainbow [35]), quickly recovers after the performance drop from weaning while larger n -step values impede learning, possibly due to stale target Q-values.

Original: These results reveal the sensitivity of prior methods in the
Revised: These results reveal the sensitivity of prior methods in the

Original: PVRL setting to speciﬁc hyperparameter choices ( n -step), indicating the need for developing stable
Revised: PVRL setting to speciﬁc hyperparameter choices ( n -step), indicating the need for developing stable

Original: PVRL methods that do not fail when weaning off the teacher.
Revised: PVRL methods that do not fail when weaning off the teacher.

Original: For practitioners, the takeaway is to consider this hyperparameter sensitivity when weaning off the teacher for reincarnation.
Revised: For practitioners, the takeaway is to consider this hyperparameter sensitivity when weaning off the teacher for reincarnation.

Original: 4.1 QDagger: A simple PVRL baseline
Revised: 4.1 QDagger: A simple PVRL baseline

Original: To address the limitations of prior approaches, we propose QDagger, a simple method for PVRL that combines Dagger [71], an interactive imitation learning algorithm, with n -step Q-learning (Figure 4, right).
Revised: To address the limitations of prior approaches, we propose QDagger, a simple method for PVRL that combines Dagger [71], an interactive imitation learning algorithm, with n -step Q-learning (Figure 4, right).

Original: Speciﬁcally, we ﬁrst pre-train the student on teacher data D T by minimizing L QDagger ( D T ) , which combines distillation loss with the TD loss, weighted by a constant λ .
Revised: Speciﬁcally, we ﬁrst pre-train the student on teacher data D T by minimizing L QDagger ( D T ) , which combines distillation loss with the TD loss, weighted by a constant λ .

Original: This pretraining phase helps the student to mimic the teacher’s state distribution, akin to the behavior cloning phase in Dagger.
Revised: This pretraining phase helps the student to mimic the teacher’s state distribution, akin to the behavior cloning phase in Dagger.

Original: After pretraining, we minimize L QDagger ( D S ) on the student’s replay D S , akin to kickstarting, where the teacher “corrects” the mistakes on the states visited by the student.
Revised: After pretraining, we minimize L QDagger ( D S ) on the student’s replay D S , akin to kickstarting, where the teacher “corrects” the mistakes on the states visited by the student.

Original: As opposed to minimizing the Dagger loss indeﬁnitely, QDagger decays the distillation loss coefﬁcient λ t ( λ 0 = λ ) as training progresses, to satisfy the weaning desiderata for PVRL.
Revised: As opposed to minimizing the Dagger loss indeﬁnitely, QDagger decays the distillation loss coefﬁcient λ t ( λ 0 = λ ) as training progresses, to satisfy the weaning desiderata for PVRL.

Original: Weaning allows QDagger to deviate from the suboptimal teacher policy π T , as opposed to being perpetually constrained to stay close to π T (Figure 9).
Revised: Weaning allows QDagger to deviate from the suboptimal teacher policy π T , as opposed to being perpetually constrained to stay close to π T (Figure 9).

Original: We ﬁnd that both decaying λ t linearly over training steps or using an afﬁne function of the ratio of student and teacher performance worked well (Appendix A.3).
Revised: We ﬁnd that both decaying λ t linearly over training steps or using an afﬁne function of the ratio of student and teacher performance worked well (Appendix A.3).

Original: Assuming the student policy π ( ·| s )
Revised: Assuming the student policy π ( ·| s )

Original: =
Revised: =

Original: softmax( Q ( s, · ) /τ ) , the QDagger loss is given by:
Revised: softmax( Q ( s, · ) /τ ) , the QDagger loss is given by:

Original: [Equation]
Revised: [Equation]

Original: Figure 2 shows that QDagger outperforms prior methods and surpasses the teacher.
Revised: Figure 2 shows that QDagger outperforms prior methods and surpasses the teacher.

Original: We remark that
Revised: We remark that

Original: DQfD can be viewed as a QDagger ablation that uses a margin loss instead of a distillation loss, while kickstarting as another ablation that does not pretrain on teacher data.
Revised: DQfD can be viewed as a QDagger ablation that uses a margin loss instead of a distillation loss, while kickstarting as another ablation that does not pretrain on teacher data.

Original: Equipped with QDagger, we show how to incorporate PVRL into our workﬂow and demonstrate its beneﬁts over tabula rasa RL.
Revised: Equipped with QDagger, we show how to incorporate PVRL into our workﬂow and demonstrate its beneﬁts over tabula rasa RL.

Original:  Reincarnating RL as a research workﬂow
Revised:  Reincarnating RL as a research workﬂow

Original: Revisiting ALE .
Revised: Revisiting ALE .

Original: As Mnih et al.
Revised: As Mnih et al.

Original: [60]’s development of Nature DQN established the tabula rasa workﬂow on ALE, we demonstrate how iterating on ALE agents’ design can be signiﬁcantly accelerated using a reincarnating RL workﬂow, starting from Nature DQN, in Figure 1.
Revised: [60]’s development of Nature DQN established the tabula rasa workﬂow on ALE, we demonstrate how iterating on ALE agents’ design can be signiﬁcantly accelerated using a reincarnating RL workﬂow, starting from Nature DQN, in Figure 1.

Original: Although Nature DQN used RMSProp, Adam yields better performance than RMSProp [1, 64].
Revised: Although Nature DQN used RMSProp, Adam yields better performance than RMSProp [1, 64].

Original: While we can train another
Revised: While we can train another

Original: DQN agent from scratch with Adam, ﬁne-tuning Nature DQN with Adam and 3 -step returns, with a reduced learning rate ( Figure 7), matches the performance of this tabula rasa DQN trained for 400M frames, using a 20 times smaller sample budget (Panel 2 in Figure 1).
Revised: DQN agent from scratch with Adam, ﬁne-tuning Nature DQN with Adam and 3 -step returns, with a reduced learning rate ( Figure 7), matches the performance of this tabula rasa DQN trained for 400M frames, using a 20 times smaller sample budget (Panel 2 in Figure 1).

Original: As such, on a P100 GPU, ﬁne-tuning only requires training for a few hours rather than a week needed for tabula rasa RL.
Revised: As such, on a P100 GPU, ﬁne-tuning only requires training for a few hours rather than a week needed for tabula rasa RL.

Original: Given this ﬁne-tuned DQN, ﬁne-tuning it further results in diminishing returns with additional frames due to being constrained to use the 3-layer convolutional neural network (CNN) with the DQN algorithm.
Revised: Given this ﬁne-tuned DQN, ﬁne-tuning it further results in diminishing returns with additional frames due to being constrained to use the 3-layer convolutional neural network (CNN) with the DQN algorithm.

Original: Let us now consider how one might use a more general reincarnation approach to improve on ﬁne-tuning, by leveraging architectural and algorithmic advances since DQN, without the sample complexity of training from scratch (Panel 3 in Figure 1).
Revised: Let us now consider how one might use a more general reincarnation approach to improve on ﬁne-tuning, by leveraging architectural and algorithmic advances since DQN, without the sample complexity of training from scratch (Panel 3 in Figure 1).

Original: Speciﬁcally, using QDagger to transfer the ﬁne-tuned DQN, we reincarnate Impala-CNN Rainbow that combines Dopamine Rainbow [35], which incorporates distributional RL [12], prioritized replay [73] and n -step returns, with an Impala-CNN architecture [26], a deep ResNet with 15 convolutional layers.
Revised: Speciﬁcally, using QDagger to transfer the ﬁne-tuned DQN, we reincarnate Impala-CNN Rainbow that combines Dopamine Rainbow [35], which incorporates distributional RL [12], prioritized replay [73] and n -step returns, with an Impala-CNN architecture [26], a deep ResNet with 15 convolutional layers.

Original: Tabula rasa Impala-CNN Rainbow outperforms ﬁne-tuning DQN further within 25M frames.
Revised: Tabula rasa Impala-CNN Rainbow outperforms ﬁne-tuning DQN further within 25M frames.

Original: Reincarnated Impala-CNN Rainbow quickly outperforms its teacher policy within 5M frames and maintains superior performance over its tabula rasa counterpart throughout training for 50M frames.
Revised: Reincarnated Impala-CNN Rainbow quickly outperforms its teacher policy within 5M frames and maintains superior performance over its tabula rasa counterpart throughout training for 50M frames.

Original: To catch up with the performance of this reincarnated agent’s performance, the tabula rasa Impala-CNN Rainbow requires additional training for 50M frames (48 hours on a P100 GPU).
Revised: To catch up with the performance of this reincarnated agent’s performance, the tabula rasa Impala-CNN Rainbow requires additional training for 50M frames (48 hours on a P100 GPU).

Original: See Appendix A.4 for more training details.
Revised: See Appendix A.4 for more training details.

Original: Overall, these results indicate how past research on ALE could have been accelerated by incorporating a reincarnating RL approach to designing agents, instead of always re-training agents from scratch.
Revised: Overall, these results indicate how past research on ALE could have been accelerated by incorporating a reincarnating RL approach to designing agents, instead of always re-training agents from scratch.

Original: Tackling a challenging control task .
Revised: Tackling a challenging control task .

Original: To show how reincarnating RL can enable faster experimentation, we apply PVRL on the humanoid:run locomotion task, one of the hardest control problems in DMC [80] due to its large action space (21 degrees of freedom).
Revised: To show how reincarnating RL can enable faster experimentation, we apply PVRL on the humanoid:run locomotion task, one of the hardest control problems in DMC [80] due to its large action space (21 degrees of freedom).

Original: For this experiment, shown in
Revised: For this experiment, shown in

Original: Figure 5, we use actor-critic agents in Acme [37].
Revised: Figure 5, we use actor-critic agents in Acme [37].

Original: For the teacher policy, we use TD3 [29] trained for 10M environment steps and pick the best run.
Revised: For the teacher policy, we use TD3 [29] trained for 10M environment steps and pick the best run.

Original: We ﬁnd that ﬁne-tuning this TD3 agent degrades performance after 15M environment steps (other learning rates in Appendix A.4), which may be related to capacity loss in value-based RL with prolonged training [47, 56].
Revised: We ﬁnd that ﬁne-tuning this TD3 agent degrades performance after 15M environment steps (other learning rates in Appendix A.4), which may be related to capacity loss in value-based RL with prolonged training [47, 56].

Original: For reincarnation, we use single-actor D4PG [8], a distributional RL variant of DDPG [54], with a larger policy and critic architecture than TD3.
Revised: For reincarnation, we use single-actor D4PG [8], a distributional RL variant of DDPG [54], with a larger policy and critic architecture than TD3.

Original: Reincarnated D4PG performs better than its tabula rasa counterpart for the ﬁrst 10M environment interactions.
Revised: Reincarnated D4PG performs better than its tabula rasa counterpart for the ﬁrst 10M environment interactions.

Original: Both these agents converge to similar performance, which is likely a limitation of QDagger.
Revised: Both these agents converge to similar performance, which is likely a limitation of QDagger.

Original: This result also raises the question of whether better PVRL methods can lead to reincarnated agents that outperform their tabula rasa counterpart throughout learning.
Revised: This result also raises the question of whether better PVRL methods can lead to reincarnated agents that outperform their tabula rasa counterpart throughout learning.

Original: Nevertheless, tabula rasa D4PG requires additional training for 10-12 hours on a V100 GPU to match reincarnated D4PG’s performance, which might quickly add up to a substantial savings in compute when running a large set of experiments ( e.g., architectural or hyperparameter sweeps).
Revised: Nevertheless, tabula rasa D4PG requires additional training for 10-12 hours on a V100 GPU to match reincarnated D4PG’s performance, which might quickly add up to a substantial savings in compute when running a large set of experiments ( e.g., architectural or hyperparameter sweeps).

Original: Balloon Learning Environment (BLE) [33].
Revised: Balloon Learning Environment (BLE) [33].

Original: One of the motivations of our work is to be able to use deep RL in real-world tasks in a data and computationally efﬁcient manner.
Revised: One of the motivations of our work is to be able to use deep RL in real-world tasks in a data and computationally efﬁcient manner.

Original: To this end, the BLE
Revised: To this end, the BLE

Original: Q R - D Q N
Revised: Q R - D Q N

Original: I Q N
Revised: I Q N

Original: R 2 D
Revised: R 2 D

Original: R e i n c a r n a t e d I Q N
Revised: R e i n c a r n a t e d I Q N

Original: R e i n c a r n a t e d
Revised: R e i n c a r n a t e d

Original: R 2 D 6 F i n e - t u n e d
Revised: R 2 D 6 F i n e - t u n e d

Original: P e r c i a t e lli *
Revised: P e r c i a t e lli *

Original: T e a c
Revised: T e a c

Original: h e r N o r m a li
Revised: h e r N o r m a li

Original: z
Revised: z

Original: e
Revised: e

Original: d S c o r e % provides a high-ﬁdelity simulator for navigating stratospheric balloons using RL [11].
Revised: d S c o r e % provides a high-ﬁdelity simulator for navigating stratospheric balloons using RL [11].

Original: An agent in
Revised: An agent in

Original: BLE can choose from three actions to control the balloon: move up, down, or stay in place.
Revised: BLE can choose from three actions to control the balloon: move up, down, or stay in place.

Original: The balloon can only move laterally by “surﬁng” the winds at its altitude; the winds change over time and vary as the balloon changes position and altitude.
Revised: The balloon can only move laterally by “surﬁng” the winds at its altitude; the winds change over time and vary as the balloon changes position and altitude.

Original: Thus, the agent is interacting with a partially observable and non-stationary system, rendering this environment quite challenging.
Revised: Thus, the agent is interacting with a partially observable and non-stationary system, rendering this environment quite challenging.

Original: For the teacher, we use the QR-DQN agent provided by BLE, called Perciatelli , trained using large-scale distributed
Revised: For the teacher, we use the QR-DQN agent provided by BLE, called Perciatelli , trained using large-scale distributed

Original: RL for 40 days on the production-level Loon simulator by Bellemare et al.
Revised: RL for 40 days on the production-level Loon simulator by Bellemare et al.

Original: [11] and further ﬁne-tuned in BLE.
Revised: [11] and further ﬁne-tuned in BLE.

Original: For our experiments, we train distributed RL agents using Acme with 64 actors for a budget of 50,000 episodes on a single cloud TPU-v2, taking approximately 10-12 hours per run.
Revised: For our experiments, we train distributed RL agents using Acme with 64 actors for a budget of 50,000 episodes on a single cloud TPU-v2, taking approximately 10-12 hours per run.

Original: In Figure 6, we compare the ﬁnal performance of distributed agents trained tabula rasa (in pink), with reincarnation (in blue), and ﬁne-tuned (in yellow).
Revised: In Figure 6, we compare the ﬁnal performance of distributed agents trained tabula rasa (in pink), with reincarnation (in blue), and ﬁne-tuned (in yellow).

Original: We consider three agents, QR-DQN [23] with an MLP architecture (same as Perciatelli), IQN [22] with a Densenet architecture [39], and a recurrent agent R2D6 2 for addressing the partial observability in BLE.
Revised: We consider three agents, QR-DQN [23] with an MLP architecture (same as Perciatelli), IQN [22] with a Densenet architecture [39], and a recurrent agent R2D6 2 for addressing the partial observability in BLE.

Original: When trained tabula rasa, none of these agents are able to match the teacher performance, with the teacher-lookalike QR-DQN agent performing particularly poorly.
Revised: When trained tabula rasa, none of these agents are able to match the teacher performance, with the teacher-lookalike QR-DQN agent performing particularly poorly.

Original: As R2D6 and IQN have substantial architectural differences from the teacher, we utilize PVRL for transferring the teacher.
Revised: As R2D6 and IQN have substantial architectural differences from the teacher, we utilize PVRL for transferring the teacher.

Original: Reincarnation allows IQN to match and R2D to surpass teacher, although both lag behind ﬁne-tuning the teacher.
Revised: Reincarnation allows IQN to match and R2D to surpass teacher, although both lag behind ﬁne-tuning the teacher.

Original: More details in Appendix A.4.2.
Revised: More details in Appendix A.4.2.

Original: When ﬁne-tuning, we are reloading the weights from Perciatelli, which was notably trained on a broader geographical region than BLE and whose training distribution can be considered a superset of what is used by the other agents; this is likely the reason that ﬁne-tuning does remarkably well relative to other agents in BLE.
Revised: When ﬁne-tuning, we are reloading the weights from Perciatelli, which was notably trained on a broader geographical region than BLE and whose training distribution can be considered a superset of what is used by the other agents; this is likely the reason that ﬁne-tuning does remarkably well relative to other agents in BLE.

Original: Efﬁciently transferring information in Perciatelli’s weights to another agent without the replay data from the Loon simulator presents an interesting challenge for future work.
Revised: Efﬁciently transferring information in Perciatelli’s weights to another agent without the replay data from the Loon simulator presents an interesting challenge for future work.

Original: Overall, the improved efﬁciency of reincarnating RL (ﬁne-tuning and PVRL) over tabula rasa RL, as evident on the BLE, could make deep RL more accessible to researchers without access to industrialscale resources as they can build upon prior computational work, such as model checkpoints, enabling the possible reuse of months of prior computation ( e.g., Perciatelli).
Revised: Overall, the improved efﬁciency of reincarnating RL (ﬁne-tuning and PVRL) over tabula rasa RL, as evident on the BLE, could make deep RL more accessible to researchers without access to industrialscale resources as they can build upon prior computational work, such as model checkpoints, enabling the possible reuse of months of prior computation ( e.g., Perciatelli).

Original:  Considerations in Reincarnating RL
Revised:  Considerations in Reincarnating RL

Original: Reincarnation via ﬁne-tuning .
Revised: Reincarnation via ﬁne-tuning .

Original: Given access to model weights and replay of a value-based agent, a simple reincarnation strategy is to ﬁne-tune this agent.
Revised: Given access to model weights and replay of a value-based agent, a simple reincarnation strategy is to ﬁne-tune this agent.

Original: While naive ﬁne-tuning with the same learning rate ( lr ) as the nearly saturated original agent does not exhibit improvement, ﬁne-tuning[Figure] [Figure] with a reduced lr , for only 1 million additional frames, results in 25% IQM improvement for
Revised: While naive ﬁne-tuning with the same learning rate ( lr ) as the nearly saturated original agent does not exhibit improvement, ﬁne-tuning with a reduced lr , for only 1 million additional frames, results in 25% IQM improvement for

Original: DQN (Adam) and 50% IQM improvement for Nature DQN trained with RMSProp (Figure 7).
Revised: DQN (Adam) and 50% IQM improvement for Nature DQN trained with RMSProp (Figure 7).

Original: As reincarnating RL leverages existing computational work ( e.g., model checkpoints), it allows us to easily experiment with such hyperparameter schedules, which can be expensive in the tabula rasa setting.
Revised: As reincarnating RL leverages existing computational work ( e.g., model checkpoints), it allows us to easily experiment with such hyperparameter schedules, which can be expensive in the tabula rasa setting.

Original: Note that when ﬁne-tuning, one is forced to keep the same network architecture; in contrast, reincarnating RL grants ﬂexibility in architecture and algorithmic choices, which can surpass ﬁne-tuning performance (Figures 1 and 5).
Revised: Note that when ﬁne-tuning, one is forced to keep the same network architecture; in contrast, reincarnating RL grants ﬂexibility in architecture and algorithmic choices, which can surpass ﬁne-tuning performance (Figures 1 and 5).

Original: Difference with tabula rasa benchmarking .
Revised: Difference with tabula rasa benchmarking .

Original: Are student agents that are more data-efﬁcient when trained from scratch also better for reincarnating RL?
Revised: Are student agents that are more data-efﬁcient when trained from scratch also better for reincarnating RL?

Original: In Figure 8, we answer this question in the negative, indicating the possibility of developing better students for utilizing existing knowledge.
Revised: In Figure 8, we answer this question in the negative, indicating the possibility of developing better students for utilizing existing knowledge.

Original: Speciﬁcally, we compare Dopamine Rainbow [35] and DrQ [90], under 
Revised: Speciﬁcally, we compare Dopamine Rainbow [35] and DrQ [90], under tabula rasa and PVRL settings.

Original: DrQ outperforms Rainbow in low-data regime when trained from scratch but underperforms Rainbow in the PVRL setting as well as when training longer from scratch.
Revised: DrQ outperforms Rainbow in low-data regime when trained from scratch but underperforms Rainbow in the PVRL setting as well as when training longer from scratch.

Original: Based on this, we speculate that reincarnating RL comparisons might be more consistent with asymptotic tabula rasa comparisons.
Revised: Based on this, we speculate that reincarnating RL comparisons might be more consistent with asymptotic tabula rasa comparisons.

Original: Reincarnation vs. Distillation .
Revised: Reincarnation vs. Distillation .

Original: PVRL is different from imitation learning or imitation-regularized
Revised: PVRL is different from imitation learning or imitation-regularized

Original: RL as it focuses on using an existing policy only as a launchpad for further learning, as opposed to imitating or staying close to it.
Revised: RL as it focuses on using an existing policy only as a launchpad for further learning, as opposed to imitating or staying close to it.

Original: To contrast these settings, we run two ablations of QDagger for reincarnating Impala-CNN Rainbow given a DQN teacher policy: (1) Dagger [71], which only minimizes the on-policy distillation loss in QDagger, and (2) Dagger + QL, which uses a ﬁxed distillation loss coefﬁcient throughout training (as opposed to QDagger, which decays it; see Equation 2).
Revised: To contrast these settings, we run two ablations of QDagger for reincarnating Impala-CNN Rainbow given a DQN teacher policy: (1) Dagger [71], which only minimizes the on-policy distillation loss in QDagger, and (2) Dagger + QL, which uses a ﬁxed distillation loss coefﬁcient throughout training (as opposed to QDagger, which decays it; see Equation 2).

Original: As shown in Figure 9, Dagger performs similarly to the teacher while Dagger + QL improves over the teacher but quickly saturates in performance.
Revised: As shown in Figure 9, Dagger performs similarly to the teacher while Dagger + QL improves over the teacher but quickly saturates in performance.

Original: On the contrary, QDagger substantially outperforms these ablations and shows continual improvement with additional environment interactions.
Revised: On the contrary, QDagger substantially outperforms these ablations and shows continual improvement with additional environment interactions.

Original: Dependency on prior work .
Revised: Dependency on prior work .

Original: While performance in reincarnating RL depend on prior computational work ( e.g., teacher policy in PVRL), this is analogous to how ﬁne-tuning results in NLP / computer vision depend on the pretrained models ( e.g., using BERT vs GPT-3).
Revised: While performance in reincarnating RL depend on prior computational work ( e.g., teacher policy in PVRL), this is analogous to how ﬁne-tuning results in NLP / computer vision depend on the pretrained models ( e.g., using BERT vs GPT-3).

Original: To investigate teacher dependence in PVRL, we reincarnate a ﬁxed student from three different DQN teachers (Figure 10).
Revised: To investigate teacher dependence in PVRL, we reincarnate a ﬁxed student from three different DQN teachers (Figure 10).

Original: As expected, we observe that a higher performing teacher results in a better performing student.
Revised: As expected, we observe that a higher performing teacher results in a better performing student.

Original: However, reincarnation from two policies with similar performance but obtained from different agents, DQN (Adam) vs. a ﬁne-tuned Nature DQN, results in different performance.
Revised: However, reincarnation from two policies with similar performance but obtained from different agents, DQN (Adam) vs. a ﬁne-tuned Nature DQN, results in different performance.

Original: This suggests that a reincarnated student’s performance depends not only on the teacher’s performance but also on its behavior.
Revised: This suggests that a reincarnated student’s performance depends not only on the teacher’s performance but also on its behavior.

Original: Nevertheless, the ranking of PVRL algorithms remains consistent across these two teacher policies (Figure A.11).
Revised: Nevertheless, the ranking of PVRL algorithms remains consistent across these two teacher policies (Figure A.11).

Original: See Section 7 for a broader discussion about generalizability.
Revised: See Section 7 for a broader discussion about generalizability.

Original:  Reproducibility, Comparisons and Generalizability in Reincarnating RL
Revised:  Reproducibility, Comparisons and Generalizability in Reincarnating RL

Original: Scientiﬁc Comparisons .
Revised: Scientiﬁc Comparisons .

Original: Fairly comparing reincarnation approaches entails using the exactly same computational work and workﬂow.
Revised: Fairly comparing reincarnation approaches entails using the exactly same computational work and workﬂow.

Original: For example, in the PVRL setting, the same teacher and data should be used when comparing different algorithms, as we do in Section 4.
Revised: For example, in the PVRL setting, the same teacher and data should be used when comparing different algorithms, as we do in Section 4.

Original: To enable this, it would be beneﬁcial if the researchers can release model checkpoints and the data generated (at least the ﬁnal replay buffers), in addition to open-source code for their trained RL agents.
Revised: To enable this, it would be beneﬁcial if the researchers can release model checkpoints and the data generated (at least the ﬁnal replay buffers), in addition to open-source code for their trained RL agents.

Original: Indeed, to allow others to use the same reincarnation setup as our work, we have already open-sourced DQN (Adam) agent checkpoints and the ﬁnal replay buffer at gs://rl_checkpoints .
Revised: Indeed, to allow others to use the same reincarnation setup as our work, we have already open-sourced DQN (Adam) agent checkpoints and the ﬁnal replay buffer at gs://rl_checkpoints .

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: Generalizability .
Revised: Generalizability .

Original: The generalizable ﬁndings in reincarnating RL would be about comparing algorithmic efﬁcacy given access to existing computational work on a task.
Revised: The generalizable ﬁndings in reincarnating RL would be about comparing algorithmic efﬁcacy given access to existing computational work on a task.

Original: As such, the performance ranking of reincarnation algorithms is likely to remain consistent across different teachers.
Revised: As such, the performance ranking of reincarnation algorithms is likely to remain consistent across different teachers.

Original: In fact
Revised: In fact

Original: [Figure]
Revised: [Figure]

Original: we empirically veriﬁed this for the PVRL setting, where we ﬁnd that while using two different teacher policies, namely DQN(Adam) vs. a ﬁne-tuned Nature DQN, leads to different performance trends but the ranking of PVRL algorithms remain consistent: QDagger > Kickstarting >
Revised: we empirically veriﬁed this for the PVRL setting, where we ﬁnd that while using two different teacher policies, namely DQN(Adam) vs. a ﬁne-tuned Nature DQN, leads to different performance trends but the ranking of PVRL algorithms remain consistent: QDagger > Kickstarting >

Original: Pretraining (see
Revised: Pretraining (see

Original: Figure 2 and Figure A.11).
Revised: Figure 2 and Figure A.11).

Original: Practitioners can use the ﬁndings from reincarnating RL to try to improve on an existing deployed RL policy (as opposed to being restricted to running tabula rasa RL).
Revised: Practitioners can use the ﬁndings from reincarnating RL to try to improve on an existing deployed RL policy (as opposed to being restricted to running tabula rasa RL).

Original: For example, this work developed QDagger using ALE and applied it to PVRL on other tasks with existing policies (Humanoid-run and BLE).
Revised: For example, this work developed QDagger using ALE and applied it to PVRL on other tasks with existing policies (Humanoid-run and BLE).

Original: Reproducibility .
Revised: Reproducibility .

Original: Reproducibility from scratch is challenging in RRL as it would require details of the generation of the prior computational work ( e.g., teacher policies), which may itself has been obtained via reincarnating RL.
Revised: Reproducibility from scratch is challenging in RRL as it would require details of the generation of the prior computational work ( e.g., teacher policies), which may itself has been obtained via reincarnating RL.

Original: As reproducibility from scratch involves reproducing existing computational work, it could be more expensive than training tabula rasa, which beats the purpose of doing reincarnation.
Revised: As reproducibility from scratch involves reproducing existing computational work, it could be more expensive than training tabula rasa, which beats the purpose of doing reincarnation.

Original: Furthermore, reproducibility from scratch is also difﬁcult in NLP and computed vision, where existing pretrained models ( e.g., , GPT-3) are rarely, if ever, reproduced / re-trained from scratch but almost always used as-is.
Revised: Furthermore, reproducibility from scratch is also difﬁcult in NLP and computed vision, where existing pretrained models ( e.g., , GPT-3) are rarely, if ever, reproduced / re-trained from scratch but almost always used as-is.

Original: Despite this difﬁculty, pretraining-and-ﬁne-tuning is a dominant paradigm in NLP and vision [ e.g., 18, 25, 34, 38], and we believe that a similar difﬁculty in
Revised: Despite this difﬁculty, pretraining-and-ﬁne-tuning is a dominant paradigm in NLP and vision [ e.g., 18, 25, 34, 38], and we believe that a similar difﬁculty in

Original: RRL should not prevent researchers from investigating and studying this important class of problems.
Revised: RRL should not prevent researchers from investigating and studying this important class of problems.

Original: Instead, we expect that RRL research would build on open-sourced prior computational work.
Revised: Instead, we expect that RRL research would build on open-sourced prior computational work.

Original: Akin to NLP and vision, where typically a small set of pretrained models are used in research, we believe that research on developing better reincarnating RL methods can also possibly converge to a small set of open-sourced models / data on a given benchmark, e.g., the agents and data we released on Atari or the 25 , 000 trained Atari agents released by Gogianu et al.
Revised: Akin to NLP and vision, where typically a small set of pretrained models are used in research, we believe that research on developing better reincarnating RL methods can also possibly converge to a small set of open-sourced models / data on a given benchmark, e.g., the agents and data we released on Atari or the 25 , 000 trained Atari agents released by Gogianu et al.

Original: [31], concurrent to this work.
Revised: [31], concurrent to this work.

Original:  Conclusion
Revised:  Conclusion

Original: Our work shows that reincarnating RL is a much computationally efﬁcient research workﬂow than tabula rasa RL and can help further democratize research.
Revised: Our work shows that reincarnating RL is a much computationally efﬁcient research workﬂow than tabula rasa RL and can help further democratize research.

Original: Nevertheless, our results also open several avenues for future work.
Revised: Nevertheless, our results also open several avenues for future work.

Original: Particularly, more research is needed for developing better PVRL methods, and extending PVRL to learn from multiple suboptimal teachers [48, 53], and enabling workﬂows that can incorporate knowledge provided in a form other than a policy, such as pretrained models [41, 79], representations [88], skills [50, 58, 68], or LLMs [3].
Revised: Particularly, more research is needed for developing better PVRL methods, and extending PVRL to learn from multiple suboptimal teachers [48, 53], and enabling workﬂows that can incorporate knowledge provided in a form other than a policy, such as pretrained models [41, 79], representations [88], skills [50, 58, 68], or LLMs [3].

Original: Furthermore, we believe that reincarnating
Revised: Furthermore, we believe that reincarnating

Original: RL would be crucial for building embodied agents in open-ended domains [7, 27, 32].
Revised: RL would be crucial for building embodied agents in open-ended domains [7, 27, 32].

Original: Aligned with this work, there have been calls for collaboratively building and continually improving large pre-trained models in NLP and vision [70].
Revised: Aligned with this work, there have been calls for collaboratively building and continually improving large pre-trained models in NLP and vision [70].

Original: We hope that this work motivates RL researchers to release computational work ( e.g., model checkpoints), which would allow others to directly build on their work.
Revised: We hope that this work motivates RL researchers to release computational work ( e.g., model checkpoints), which would allow others to directly build on their work.

Original: In this regards, we have open-sourced our code and trained agents with their ﬁnal replay.
Revised: In this regards, we have open-sourced our code and trained agents with their ﬁnal replay.

Original: Furthermore, re-purposing existing benchmarks, akin to how we use ALE in this work, can serve as testbeds for reincarnating RL.
Revised: Furthermore, re-purposing existing benchmarks, akin to how we use ALE in this work, can serve as testbeds for reincarnating RL.

Original: As Newton put it “If I have seen further it is by standing on the shoulders of giants”, we argue that reincarnating RL can substantially accelerate progress by building on prior computational work, as opposed to always redoing this work from scratch.
Revised: As Newton put it “If I have seen further it is by standing on the shoulders of giants”, we argue that reincarnating RL can substantially accelerate progress by building on prior computational work, as opposed to always redoing this work from scratch.

Original: Societal Impacts
Revised: Societal Impacts

Original: Reincarnating RL could positively impact society by reducing the computational burden on researchers and is more environment friendly than tabula rasa RL.
Revised: Reincarnating RL could positively impact society by reducing the computational burden on researchers and is more environment friendly than tabula rasa RL.

Original: For example, reincarnating RL allow researchers to train super-human Atari agents on a single GPU within a span of few hours as opposed to training for a few days.
Revised: For example, reincarnating RL allow researchers to train super-human Atari agents on a single GPU within a span of few hours as opposed to training for a few days.

Original: Additionally, reincarnating RL is more accessible to the wider research community, as researchers without sufﬁcient compute resources can build on prior computational work from resource-rich groups, and even improve upon them using limited resources.
Revised: Additionally, reincarnating RL is more accessible to the wider research community, as researchers without sufﬁcient compute resources can build on prior computational work from resource-rich groups, and even improve upon them using limited resources.

Original: Furthermore, this democratization could directly improve RL applicability for practical applications, as most businesses that could beneﬁt from RL often cannot afford the expertise to design in-house solutions.
Revised: Furthermore, this democratization could directly improve RL applicability for practical applications, as most businesses that could beneﬁt from RL often cannot afford the expertise to design in-house solutions.

Original: However, this democratization could also make it easier to apply RL for potentially harmful applications.
Revised: However, this democratization could also make it easier to apply RL for potentially harmful applications.

Original: Furthermore, reincarnating RL could carry forward the bias or undesirable traits from the previously learned systems.
Revised: Furthermore, reincarnating RL could carry forward the bias or undesirable traits from the previously learned systems.

Original: As such, we urge practitioners to be mindful of how RL ﬁts into the wider socio-technical context of its deployment.
Revised: As such, we urge practitioners to be mindful of how RL ﬁts into the wider socio-technical context of its deployment.

Original: Acknowledgments
Revised: Acknowledgments

Original: We would like to thank David Ha, Evgenii Nikishin, Karol Hausman, Bobak Shahriari, Richard Song,
Revised: We would like to thank David Ha, Evgenii Nikishin, Karol Hausman, Bobak Shahriari, Richard Song,

Original: Alex Irpan, Andrey Kurenkov for their valuable feedback on this work.
Revised: Alex Irpan, Andrey Kurenkov for their valuable feedback on this work.

Original: We thank Joshua Greaves for helping us set up RL agents for BLE.
Revised: We thank Joshua Greaves for helping us set up RL agents for BLE.

Original: We also acknowledge Ted Xiao, Dale Schuurmans, Aleksandra
Revised: We also acknowledge Ted Xiao, Dale Schuurmans, Aleksandra

Original: Faust, George Tucker, Rebecca Roelofs, Eugene Brevdo, Pierluca D’Oro, Nathan Rahn, Adrien Ali
Revised: Faust, George Tucker, Rebecca Roelofs, Eugene Brevdo, Pierluca D’Oro, Nathan Rahn, Adrien Ali

Original: Taiga, Bogdan Mazoure, Jacob Buckman, Georg Ostrovski and Aviral Kumar for useful discussions.
Revised: Taiga, Bogdan Mazoure, Jacob Buckman, Georg Ostrovski and Aviral Kumar for useful discussions.

Original: Author Contributions
Revised: Author Contributions

Original: Rishabh Agarwal led the project from start-to-ﬁnish, deﬁned the scope of the work to focus on policy to value reincarnation, came up with a successful algorithm for PVRL, and performed the literature survey.
Revised: Rishabh Agarwal led the project from start-to-ﬁnish, deﬁned the scope of the work to focus on policy to value reincarnation, came up with a successful algorithm for PVRL, and performed the literature survey.

Original: He designed, implemented and ran most of the experiments on ALE, Humanoid-run and BLE, and wrote the paper.
Revised: He designed, implemented and ran most of the experiments on ALE, Humanoid-run and BLE, and wrote the paper.

Original: Max Schwarzer helped run DQfD experiments on ALE and as well as setting up some agents for the BLE codebase with Acme, was involved in project discussions and edited the paper.
Revised: Max Schwarzer helped run DQfD experiments on ALE and as well as setting up some agents for the BLE codebase with Acme, was involved in project discussions and edited the paper.

Original: Work done as a student researcher at Google.
Revised: Work done as a student researcher at Google.

Original: Pablo Samuel Castro was involved in project discussions, helped in setting up the BLE environment and implemented the initial Acme agents, and helped with paper editing.
Revised: Pablo Samuel Castro was involved in project discussions, helped in setting up the BLE environment and implemented the initial Acme agents, and helped with paper editing.

Original: Aaron Courville advised the project, helped with project direction and provided feedback on writing.
Revised: Aaron Courville advised the project, helped with project direction and provided feedback on writing.

Original: Marc Bellemare advised the project, challenged Rishabh to come up with an experimental paradigm in which one continuously improves on an existing agent, and provided feedback on writing.
Revised: Marc Bellemare advised the project, challenged Rishabh to come up with an experimental paradigm in which one continuously improves on an existing agent, and provided feedback on writing.

Original: Checklist
Revised: Checklist

Original: For all authors... (a) Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contributions and scope?
Revised: For all authors... (a) Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contributions and scope?

Original: [Yes] (b) Did you describe the limitations of your work?
Revised: [Yes] (b) Did you describe the limitations of your work?

Original: [Yes] Section 5 (BLE and continuous control results) and reproducibility and evaluation concerns in Sec(c)
Revised: [Yes] Section 5 (BLE and continuous control results) and reproducibility and evaluation concerns in Sec(c)

Original: Did you discuss any potential negative societal impacts of your work?
Revised: Did you discuss any potential negative societal impacts of your work?

Original: [Yes] (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?
Revised: [Yes] (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?

Original: [Yes] 2.
Revised: [Yes] 2.

Original: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?
Revised: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A] (b) Did you include complete proofs of all theoretical results?
Revised: [N/A] (b) Did you include complete proofs of all theoretical results?

Original: [N/A] 3.
Revised: [N/A] 3.

Original: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
Revised: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?

Original: [Yes] agarwl.github.io/reincarnating_rl .
Revised: [Yes] agarwl.github.io/reincarnating_rl .

Original: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?
Revised: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Original: [Yes] See Appendix A.3 and A. (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?
Revised: [Yes] See Appendix A.3 and A. (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [Yes] 95% CIs (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?
Revised: [Yes] 95% CIs (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?

Original: [Yes] See Appendix A. 4.
Revised: [Yes] See Appendix A. 4.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] (b) Did you mention the license of the assets?
Revised: [Yes] (b) Did you mention the license of the assets?

Original: [Yes] Apache License, Version 2.
Revised: [Yes] Apache License, Version 2.

Original: (c) Did you include any new assets either in the supplemental material or as a URL?
Revised: (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [Yes] (d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating?
Revised: [Yes] (d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating?

Original: [N/A] (e) Did you discuss whether the data you are using/curating contains personally identiﬁable information or offensive content?
Revised: [N/A] (e) Did you discuss whether the data you are using/curating contains personally identiﬁable information or offensive content?

Original: [N/A]
Revised: [N/A]

Original: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?
Revised: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?

Original: [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
Revised: [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?

Original: [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
Revised: [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?

Original: [N/A]
Revised: [N/A]

Original: A Appendix A.1 AlphaStar cost estimation
Revised: A Appendix A.1 AlphaStar cost estimation

Original: We estimate the cost of AlphaStar [85] based on the following description in the paper: “In StarCraft, each player chooses one of three races — Terran, Protoss or Zerg — each with distinct mechanics.
Revised: We estimate the cost of AlphaStar [85] based on the following description in the paper: “In StarCraft, each player chooses one of three races — Terran, Protoss or Zerg — each with distinct mechanics.

Original: We trained the league using three main agents (one for each StarCraft race), three main exploiter agents (one for each race), and six league exploiter agents (two for each race).
Revised: We trained the league using three main agents (one for each StarCraft race), three main exploiter agents (one for each race), and six league exploiter agents (two for each race).

Original: Each agent was trained using 32 third-generation tensor processing units (TPUv3) over 44 days.”
Revised: Each agent was trained using 32 third-generation tensor processing units (TPUv3) over 44 days.”

Original: This corresponds to a total of 12 agents (= 3 main + 3 exploiter + 6 league) trained for a total of 1056 TPU hours = 44 days * 24 hours/day on 32 TPU v3 chips.
Revised: This corresponds to a total of 12 agents (= 3 main + 3 exploiter + 6 league) trained for a total of 1056 TPU hours = 44 days * 24 hours/day on 32 TPU v3 chips.

Original: As per current pricing at https://cloud.google.com/tpu/pricing , TPUv3 (v3-8) cost $8 per hour.
Revised: As per current pricing at https://cloud.google.com/tpu/pricing , TPUv3 (v3-8) cost $8 per hour.

Original: Based on this, we estimate the cost of replicating AlphaStar results for an independent researcher would be at 1056 ∗ 12 ∗ 32 ∗ $8 = $3 , 244 , 032 .
Revised: Based on this, we estimate the cost of replicating AlphaStar results for an independent researcher would be at 1056 ∗ 12 ∗ 32 ∗ $8 = $3 , 244 , 032 .

Original: Please note that we are only considering the cost of replication and not accounting for other costs such as hyperparameter tuning and evaluation.
Revised: Please note that we are only considering the cost of replication and not accounting for other costs such as hyperparameter tuning and evaluation.

Original: A.2 Compute resources for PVRL experiments
Revised: A.2 Compute resources for PVRL experiments

Original: For experiments in section 4, we used a P100 GPU.
Revised: For experiments in section 4, we used a P100 GPU.

Original: For obtaining the teacher policy, the cost of running the tabula rasa DQN for 400M frames for 10 games on 3 seeds each roughly amounts to 7 days x 30 = 210 days of compute on a P100 GPU.
Revised: For obtaining the teacher policy, the cost of running the tabula rasa DQN for 400M frames for 10 games on 3 seeds each roughly amounts to 7 days x 30 = 210 days of compute on a P100 GPU.

Original: For each of the PVRL methods, we trained on 10 games with 3 runs each for 10M frames, which roughly translates to 4-5 hours.
Revised: For each of the PVRL methods, we trained on 10 games with 3 runs each for 10M frames, which roughly translates to 4-5 hours.

Original: For ofﬂine pretraining, we train methods for 1 million gradient steps with a batch size of 32, which roughly amounts to 6-7 hours (this could be further sped up by using large-batch sizes).
Revised: For ofﬂine pretraining, we train methods for 1 million gradient steps with a batch size of 32, which roughly amounts to 6-7 hours (this could be further sped up by using large-batch sizes).

Original: We list the number of conﬁgurations we evaluated for each method below.
Revised: We list the number of conﬁgurations we evaluated for each method below.

Original: • Rehearsal: We tried 5 values of teacher data ratio ρ × 4 n -step values, amounting to a total of 20 conﬁgurations.
Revised: • Rehearsal: We tried 5 values of teacher data ratio ρ × 4 n -step values, amounting to a total of 20 conﬁgurations.

Original: • JSRL:
Revised: • JSRL:

Original: We tried 4 values of teacher roll-in steps α × 2 values of decay parameter β × 2 values of n -step, amounting to 16 conﬁgurations.
Revised: We tried 4 values of teacher roll-in steps α × 2 values of decay parameter β × 2 values of n -step, amounting to 16 conﬁgurations.

Original: • RL Pretraining: We tried 2 values of λ × 4 values of n -step, amounting to 8 conﬁgurations.
Revised: • RL Pretraining: We tried 2 values of λ × 4 values of n -step, amounting to 8 conﬁgurations.

Original: • Kickstarting: We report results for 4 values of n -step for a speciﬁc temperature and distillation loss coefﬁcient.
Revised: • Kickstarting: We report results for 4 values of n -step for a speciﬁc temperature and distillation loss coefﬁcient.

Original: For hyperparameter tuning, we evaluated 2 temperature values and 2 loss coefﬁcients with a speciﬁc n -step.
Revised: For hyperparameter tuning, we evaluated 2 temperature values and 2 loss coefﬁcients with a speciﬁc n -step.

Original: Overall, this corresponds to a total of 8 conﬁgurations.
Revised: Overall, this corresponds to a total of 8 conﬁgurations.

Original: • DQfD: We report results for 4 values of n -step × 2 values of margin loss coefﬁcients × 2 values of margin parameters, amounting to 16 conﬁgurations.
Revised: • DQfD: We report results for 4 values of n -step × 2 values of margin loss coefﬁcients × 2 values of margin parameters, amounting to 16 conﬁgurations.

Original: QDagger: We report results for 4 n -step values for a speciﬁc temperature and distillation loss coefﬁcient.
Revised: QDagger: We report results for 4 n -step values for a speciﬁc temperature and distillation loss coefﬁcient.

Original: For hyperparameter tuning, we evaluated 2 different temperature and loss coefﬁcients with a speciﬁc n -step, akin to kickstarting.
Revised: For hyperparameter tuning, we evaluated 2 different temperature and loss coefﬁcients with a speciﬁc n -step, akin to kickstarting.

Original: Overall, this amounts to 8 conﬁgurations.
Revised: Overall, this amounts to 8 conﬁgurations.

Original: Based on the above, we evaluated a total of 60 (= 20+16+16+8 ) conﬁgurations without pretraining while 32 conﬁgurations with pretraining.
Revised: Based on the above, we evaluated a total of 60 (= 20+16+16+8 ) conﬁgurations without pretraining while 32 conﬁgurations with pretraining.

Original: Each of these conﬁgurations was evaluated for 30 seeds.
Revised: Each of these conﬁgurations was evaluated for 30 seeds.

Original: This amounts to a total compute time of 300-375 days for runs without pretraining on ofﬂine data while 400-480 days of GPU compute for runs involving pretraining, resulting in a total compute time of around 700 - 855 days on a P100 GPU.
Revised: This amounts to a total compute time of 300-375 days for runs without pretraining on ofﬂine data while 400-480 days of GPU compute for runs involving pretraining, resulting in a total compute time of around 700 - 855 days on a P100 GPU.

Original: A.3 PVRL: Experimental details
Revised: A.3 PVRL: Experimental details

Original: Atari 2600 Games : The subset of games in the paper includes games from the original Atari training set used by Bellemare et al.
Revised: Atari 2600 Games : The subset of games in the paper includes games from the original Atari training set used by Bellemare et al.

Original: [10] (Asterix, Beam Rider, Seaquest and Space Invaders) as well as validation games used by Mnih et al.
Revised: [10] (Asterix, Beam Rider, Seaquest and Space Invaders) as well as validation games used by Mnih et al.

Original: [60] (Breakout, Enduro, River Raid), except the games which are nearly solved by DQN, such as Freeway and Pong.
Revised: [60] (Breakout, Enduro, River Raid), except the games which are nearly solved by DQN, such as Freeway and Pong.

Original: We do not use any hard exploration games as a DQN teacher does not provide a meaningful teacher policy for such games.
Revised: We do not use any hard exploration games as a DQN teacher does not provide a meaningful teacher policy for such games.

Original: The remaining three games were chosen to test the student agent in environments with challenging characteristics such as requiring planning as opposed to being reactive ( e.g., Ms Pacman, Q ∗ Bert), and sparse-reward games that require long-term predictions (Bowling).
Revised: The remaining three games were chosen to test the student agent in environments with challenging characteristics such as requiring planning as opposed to being reactive ( e.g., Ms Pacman, Q ∗ Bert), and sparse-reward games that require long-term predictions (Bowling).

Original: Furthermore, most of these games can be signiﬁcantly improved over the teacher DQN performance, which is sub-human on half of the games (Ms Pacman,
Revised: Furthermore, most of these games can be signiﬁcantly improved over the teacher DQN performance, which is sub-human on half of the games (Ms Pacman,

Original: Q ∗ Bert, Bowling, Seaquest and Beam Rider).
Revised: Q ∗ Bert, Bowling, Seaquest and Beam Rider).

Original: Refer to Table A.2 for per-game teacher scores.
Revised: Refer to Table A.2 for per-game teacher scores.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: Common hyperparameters .
Revised: Common hyperparameters .

Original: We list the hyperparameters shared by all PVRL methods in Table A.1.
Revised: We list the hyperparameters shared by all PVRL methods in Table A.1.

Original: For all methods, we swept
Revised: For all methods, we swept

Original: over n -step returns in { 1 , 3 , 5 , 10 } except for DQfD [36], which originally used 10 -step returns, where we only tried 3 -step and 10 -step returns and JSRL for which we tried only 1 -step and 3 -step returns.
Revised: over n -step returns in { 1 , 3 , 5 , 10 } except for DQfD [36], which originally used 10 -step returns, where we only tried 3 -step and 10 -step returns and JSRL for which we tried only 1 -step and 3 -step returns.

Original: For PVRL methods without any pretraining phase, we use a learning rate of 6 .
Revised: For PVRL methods without any pretraining phase, we use a learning rate of 6 .

Original: 25 e − 5 (JSRL, Rehearsal), following the hyperparameter conﬁguration for Dopamine [15].
Revised: 25 e − 5 (JSRL, Rehearsal), following the hyperparameter conﬁguration for Dopamine [15].

Original: For methods that pretrain on ofﬂine data, we sweep over { 6 .
Revised: For methods that pretrain on ofﬂine data, we sweep over { 6 .

Original: e − 5 , 1 e − 5 } and found the learning rate of 1 e − 5 to perform better in our early experimentation and use it for our main results.
Revised: e − 5 , 1 e − 5 } and found the learning rate of 1 e − 5 to perform better in our early experimentation and use it for our main results.

Original: We discuss the method speciﬁc hyperparameters below.
Revised: We discuss the method speciﬁc hyperparameters below.

Original: For obtaining the teacher policy using value-based agent, we use the softmax( Q T ( s, · ) /τ ) over the teacher’s Q-function Q T and use the same temperature coefﬁcient τ for both the student and teacher policy.
Revised: For obtaining the teacher policy using value-based agent, we use the softmax( Q T ( s, · ) /τ ) over the teacher’s Q-function Q T and use the same temperature coefﬁcient τ for both the student and teacher policy.

Original: • Rehearsal : We tried 5 different values of the teacher data ratio ( ρ ) in { 0 , 1 / 256 , 1 / 64 , 1 / 16 , 1 / 4 } .
Revised: • Rehearsal : We tried 5 different values of the teacher data ratio ( ρ ) in { 0 , 1 / 256 , 1 / 64 , 1 / 16 , 1 / 4 } .

Original: The loss, L Rehearsal , can be written as: L Rehearsal =
Revised: The loss, L Rehearsal , can be written as: L Rehearsal =

Original: ρ L TD ( D T )
Revised: ρ L TD ( D T )

Original: + (1 − ρ )
Revised: + (1 − ρ )

Original: L TD ( D S ) .
Revised: L TD ( D S ) .

Original: As can be seen from the results in Figure A.12, we ﬁnd a small value of teacher data ratio ( ρ = 1 / 16 ) with 3 -step returns to be the best performing conﬁguration.
Revised: As can be seen from the results in Figure A.12, we ﬁnd a small value of teacher data ratio ( ρ = 1 / 16 ) with 3 -step returns to be the best performing conﬁguration.

Original: • JSRL .
Revised: • JSRL .

Original: As shown in Figure 4 (left), we swept over the maximum number of teacher roll in steps of α in { 0 , 100 , 1000 , 5000 } , and the decay parameter β , which governs how fast we decay the roll-in steps, in { 0 . 8 , 1 . 0 } .
Revised: As shown in Figure 4 (left), we swept over the maximum number of teacher roll in steps of α in { 0 , 100 , 1000 , 5000 } , and the decay parameter β , which governs how fast we decay the roll-in steps, in { 0 . 8 , 1 . 0 } .

Original: Note that β = 1 . 

Revised: Note that β = 1 .

Original: corresponds to JSRL-Random, which was found to be competitive in performance to JSRL [83].
Revised: corresponds to JSRL-Random, which was found to be competitive in performance to JSRL [83].

Original: [Table]
Revised: [Table]

Original: • RL Pretraining : We use CQL, which optimizes the following loss:
Revised: • RL Pretraining : We use CQL, which optimizes the following loss:

Original: [Equation]
Revised: [Equation]

Original: The choice of CQL is motivated by its simplicity as well as recent ﬁndings that ofﬂine RL methods that do not estimate the behavior policy are more suited for online ﬁne-tuning [63]
Revised: The choice of CQL is motivated by its simplicity as well as recent ﬁndings that ofﬂine RL methods that do not estimate the behavior policy are more suited for online ﬁne-tuning [63]

Original: [Table]
Revised: [Table]

Original: n
Revised: n

Original: [Table]
Revised: [Table]

Original: n = n = n =
Revised: n = n = n =

Original: [Figure]
Revised: [Figure]

Original: I Q M
Revised: I Q M

Original: N o r m a li
Revised: N o r m a li

Original: z e d
Revised: z e d

Original: S c
Revised: S c

Original: o r e
Revised: o r e

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: I
Revised: I

Original: [Figure]
Revised: [Figure]

Original: N
Revised: N

Original: [Figure]
Revised: [Figure]

Original: r m a li z e d S c
Revised: r m a li z e d S c

Original: o r e
Revised: o r e

Original: Tabula Rasa Impala-CNN Rainbow
Revised: Tabula Rasa Impala-CNN Rainbow

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: Online
Revised: Online

Original: [Figure]
Revised: [Figure]

Original: We tried two different values of CQL coefﬁcient λ ( 0 . 3 and 1 . 0 ), as shown in Figure A.13, and report the results for the better performing coefﬁcient ( λ = 0 . 3 ) in the main paper.
Revised: We tried two different values of CQL coefﬁcient λ ( 0 . 3 and 1 . 0 ), as shown in Figure A.13, and report the results for the better performing coefﬁcient ( λ = 0 . 3 ) in the main paper.

Original: • Kickstarting .
Revised: • Kickstarting .

Original: Kickstarting [74] uses the same loss as QDagger (Equation 2), but as discussed in the main paper, kickstarting does not have any pretraining phase on ofﬂine data.
Revised: Kickstarting [74] uses the same loss as QDagger (Equation 2), but as discussed in the main paper, kickstarting does not have any pretraining phase on ofﬂine data.

Original: For the temperature hyperparameter τ for obtaining the policy π ( ·| s ) =
Revised: For the temperature hyperparameter τ for obtaining the policy π ( ·| s ) =

Original: softmax( Q ( s, · ) /τ ) , we tried 0 .
Revised: softmax( Q ( s, · ) /τ ) , we tried 0 .

Original: 1 and 1 . 0 .
Revised: 1 and 1 . 0 .

Original: Similarly, we swept over two initial values for distillation loss coefﬁcient ( λ 0 ), namely 1 . 0 and 3 . 0 .
Revised: Similarly, we swept over two initial values for distillation loss coefﬁcient ( λ 0 ), namely 1 . 0 and 3 . 0 .

Original: For experiments with the DQN student, we found the coefﬁcient 3 . 0 and temperature 0 .
Revised: For experiments with the DQN student, we found the coefﬁcient 3 . 0 and temperature 0 .

Original: 1 to perform the best.
Revised: 1 to perform the best.

Original: • DQfD .
Revised: • DQfD .

Original: Following Hester et al.
Revised: Following Hester et al.

Original: [36], DQfD uses the following loss for training:
Revised: [36], DQfD uses the following loss for training:

Original: [Equation]
Revised: [Equation]

Original: where η t corresponds to the margin loss coefﬁcient, a T ( s ) = argmax a π T ( a | s ) and f ( a T , a ) is a margin function that is 0 when a = a T and a positive margin m otherwise.
Revised: where η t corresponds to the margin loss coefﬁcient, a T ( s ) = argmax a π T ( a | s ) and f ( a T , a ) is a margin function that is 0 when a = a T and a positive margin m otherwise.

Original: We swept over the values { 1 . 0 , 3 . 0 } for both the margin parameter m and initial values η 0 of the margin loss coefﬁcient η t .
Revised: We swept over the values { 1 . 0 , 3 . 0 } for both the margin parameter m and initial values η 0 of the margin loss coefﬁcient η t .

Original: For the DQN student, we report the results for the better performing margin coefﬁcients in the main paper.
Revised: For the DQN student, we report the results for the better performing margin coefﬁcients in the main paper.

Original: • QDagger .
Revised: • QDagger .

Original: Akin to kickstarting, we swept over the values of temperature τ in { 0 . 1 , 1 . 0 } and distillation coefﬁcient λ 0 in { 1 . 0 , 3 . 0 } .
Revised: Akin to kickstarting, we swept over the values of temperature τ in { 0 . 1 , 1 . 0 } and distillation coefﬁcient λ 0 in { 1 . 0 , 3 . 0 } .

Original: For ALE experiments, we decay the distillation loss coefﬁcient every training iteration (1M environment frames) using the fraction of expected returns obtained by the student policy π compared to the teacher policy π T , that is, λ t = 1 t<t 0 max(1 − G π /G πT , 0) .
Revised: For ALE experiments, we decay the distillation loss coefﬁcient every training iteration (1M environment frames) using the fraction of expected returns obtained by the student policy π compared to the teacher policy π T , that is, λ t = 1 t<t 0 max(1 − G π /G πT , 0) .

Original: For fair comparisons with other methods, we use the same strategy for decaying the distillation loss coefﬁcient λ t for Kickstarting and the margin loss coefﬁcient η t for DQfD.
Revised: For fair comparisons with other methods, we use the same strategy for decaying the distillation loss coefﬁcient λ t for Kickstarting and the margin loss coefﬁcient η t for DQfD.

Original: A.4 Reincarnating RL as a workﬂow: Additional details
Revised: A.4 Reincarnating RL as a workﬂow: Additional details

Original: Revisting ALE .
Revised: Revisting ALE .

Original: We used the ﬁnal model checkpoints of Nature DQN [60] from Agarwal et al.
Revised: We used the ﬁnal model checkpoints of Nature DQN [60] from Agarwal et al.

Original: [1], which was trained for 200M frames using the hyperparameters in Dopamine [15].
Revised: [1], which was trained for 200M frames using the hyperparameters in Dopamine [15].

Original: The ﬁne-tuned
Revised: The ﬁne-tuned

Original: DQN (Adam) in panel 2 in Figure 1 uses 3 -step returns.
Revised: DQN (Adam) in panel 2 in Figure 1 uses 3 -step returns.

Original: For the tabula rasa Impala-CNN Rainbow, we use similar hyperparameters to Dopamine Rainbow except for learning rate ( lr ), for which we ran a sweep over { 1 e − 4 , 1 e − 5 , 3 e − 5 } , shown in Figure A.14, and use the best performing lr of 3 e − 5 .
Revised: For the tabula rasa Impala-CNN Rainbow, we use similar hyperparameters to Dopamine Rainbow except for learning rate ( lr ), for which we ran a sweep over { 1 e − 4 , 1 e − 5 , 3 e − 5 } , shown in Figure A.14, and use the best performing lr of 3 e − 5 .

Original: For the reincarnated Impala-CNN Rainbow in Panel 3, we use a QDagger distillation coefﬁcient of 1 . 0 and sweep over temperature parameter τ in { 0 . 1 , 1 . 0 } , as shown in Figure A.15.
Revised: For the reincarnated Impala-CNN Rainbow in Panel 3, we use a QDagger distillation coefﬁcient of 1 . 0 and sweep over temperature parameter τ in { 0 . 1 , 1 . 0 } , as shown in Figure A.15.

Original: Consistent with our other ﬁne-tuning results on ALE, in Panel 3, using a reduced lr of 3 e − 6 for ﬁne-tuning the already ﬁne-tuned DQN agent results in better performance, compared to using an lr of 1 e − 5 , as used by ﬁne-tuned DQN.
Revised: Consistent with our other ﬁne-tuning results on ALE, in Panel 3, using a reduced lr of 3 e − 6 for ﬁne-tuning the already ﬁne-tuned DQN agent results in better performance, compared to using an lr of 1 e − 5 , as used by ﬁne-tuned DQN.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: l
Revised: l

Original: [Figure]
Revised: [Figure]

Original: a t i o
Revised: a t i o

Original: [Figure]
Revised: [Figure]

Original: p i s o d e r e t u r n
Revised: p i s o d e r e t u r n

Original: [Figure]
Revised: [Figure]

Original: All the different learning rates exhibit similar perfor- mance trends including severe degradation after prolonged training
Revised: All the different learning rates exhibit similar perfor- mance trends including severe degradation after prolonged training

Original: [Figure]
Revised: [Figure]

Original: A.4.1 Humanoid:Run
Revised: A.4.1 Humanoid:Run

Original: The purpose of humanoid:run experiments is to show the utility of reincarnation in a complex continuous control environment given access to a pretrained policy and some data from its ﬁnal replay buffer.
Revised: The purpose of humanoid:run experiments is to show the utility of reincarnation in a complex continuous control environment given access to a pretrained policy and some data from its ﬁnal replay buffer.

Original: Irrespective of performance from ﬁne-tuning performance TD3, we demonstrate the beneﬁts of using reincarnation over tabula rasa D4PG.
Revised: Irrespective of performance from ﬁne-tuning performance TD3, we demonstrate the beneﬁts of using reincarnation over tabula rasa D4PG.

Original: For example, reincarnated D4PG achieves performance obtained by SAC in 10M frames 3 in only half the number of samples ( i.e., 5M frames).
Revised: For example, reincarnated D4PG achieves performance obtained by SAC in 10M frames 3 in only half the number of samples ( i.e., 5M frames).

Original: For obtaining the pretrained policy, TD3 was chosen as (1) it’s a well-known method for continuous control, and (2) we could use an off-the-shelf JAX implementation in Acme, which is competitive on humanoid-run.
Revised: For obtaining the pretrained policy, TD3 was chosen as (1) it’s a well-known method for continuous control, and (2) we could use an off-the-shelf JAX implementation in Acme, which is competitive on humanoid-run.

Original: For tabula rasa TD3 [29], we used a learning rate ( lr ) of 3 e − 4 for both the policy and critic, which are represented using a MLP with 2 hidden layers of size (256, 256).
Revised: For tabula rasa TD3 [29], we used a learning rate ( lr ) of 3 e − 4 for both the policy and critic, which are represented using a MLP with 2 hidden layers of size (256, 256).

Original: For other hyperparameters, we used the default values in Acme’s TD3 implementation.
Revised: For other hyperparameters, we used the default values in Acme’s TD3 implementation.

Original: For ﬁne-tuning TD3, we use the last 500K environment steps from the TD3’s replay buffer and use the same hyperparameters as tabula rasa TD3 except for lr .
Revised: For ﬁne-tuning TD3, we use the last 500K environment steps from the TD3’s replay buffer and use the same hyperparameters as tabula rasa TD3 except for lr .

Original: Speciﬁcally, we swept over the lr in { 1 e − 4 , 3 e − 4 , 3 e − 05 } , shown in Figure A.17, and ﬁnd that all lr s exhibit performance degradation with prolonged training.
Revised: Speciﬁcally, we swept over the lr in { 1 e − 4 , 3 e − 4 , 3 e − 05 } , shown in Figure A.17, and ﬁnd that all lr s exhibit performance degradation with prolonged training.

Original: We hypothesize that this degradation is likely caused by network capacity loss with prolonged training in value-based RL methods [47, 56].
Revised: We hypothesize that this degradation is likely caused by network capacity loss with prolonged training in value-based RL methods [47, 56].

Original: We believe that this issue does not affect our conclusions about the efﬁcacy of reincarnating RL over a tabula rasa workﬂow.
Revised: We believe that this issue does not affect our conclusions about the efﬁcacy of reincarnating RL over a tabula rasa workﬂow.

Original: Further investigation of this performance degradation is outside the scope of the present work.
Revised: Further investigation of this performance degradation is outside the scope of the present work.

Original: For the tabula rasa D4PG [8], we use MLP networks with 3 hidden layers of size (256 , 256 , 256) for the policy and (512 , 512 , 256) for the critic.
Revised: For the tabula rasa D4PG [8], we use MLP networks with 3 hidden layers of size (256 , 256 , 256) for the policy and (512 , 512 , 256) for the critic.

Original: We used 3 e − 4 as the learning rate and a sigma value of 0 . 2 that sets the variance of the Gaussian noise to the behavior policy.
Revised: We used 3 e − 4 as the learning rate and a sigma value of 0 . 2 that sets the variance of the Gaussian noise to the behavior policy.

Original: Other hyperparameters use the default values for D4PG implementation in Acme.
Revised: Other hyperparameters use the default values for D4PG implementation in Acme.

Original: For reincarnating D4PG using QDagger, we minimize a distillation loss between the D4PG’s actor policy and the teacher policy from TD3 jointly with the actor-critic losses.
Revised: For reincarnating D4PG using QDagger, we minimize a distillation loss between the D4PG’s actor policy and the teacher policy from TD3 jointly with the actor-critic losses.

Original: For QDagger speciﬁc hyperparameters, we pretrain using 200K gradient updates as well as decay λ t to 0 over a period of 200K gradient updates during the online training phase.
Revised: For QDagger speciﬁc hyperparameters, we pretrain using 200K gradient updates as well as decay λ t to 0 over a period of 200K gradient updates during the online training phase.

Original: Additionally, we sweep over distillation coefﬁcient λ 0 in { 0 . 1 , 0 . 3 } , as shown in Figure A.18.
Revised: Additionally, we sweep over distillation coefﬁcient λ 0 in { 0 . 1 , 0 . 3 } , as shown in Figure A.18.

Original: Note that both TD3 and D4PG use 5 -step returns by default in Acme.
Revised: Note that both TD3 and D4PG use 5 -step returns by default in Acme.

Original: A.4.2 Balloon Learning Environment (BLE)
Revised: A.4.2 Balloon Learning Environment (BLE)

Original: Details about BLE can be found in [33].
Revised: Details about BLE can be found in [33].

Original: For self-containedness, we include important details below.
Revised: For self-containedness, we include important details below.

Original: Station Keeping .
Revised: Station Keeping .

Original: Stratospheric balloons are ﬁlled with a buoyant gas that allows them to ﬂoat for weeks or months at a time in the stratosphere, about twice as high as a passenger plane’s cruising altitude.
Revised: Stratospheric balloons are ﬁlled with a buoyant gas that allows them to ﬂoat for weeks or months at a time in the stratosphere, about twice as high as a passenger plane’s cruising altitude.

Original: Though there are many potential variations of stratospheric balloons, the kind emulated in the BLE are equipped with solar panels and batteries, which allow them to adjust their altitude by controlling the weight of air in their ballast using an electric pump.
Revised: Though there are many potential variations of stratospheric balloons, the kind emulated in the BLE are equipped with solar panels and batteries, which allow them to adjust their altitude by controlling the weight of air in their ballast using an electric pump.

Original: However, they have no means to propel themselves laterally, which means that they are subject to wind patterns in the air around them.
Revised: However, they have no means to propel themselves laterally, which means that they are subject to wind patterns in the air around them.

Original: By changing its altitude, a stratospheric balloon can surf winds moving in different directions.
Revised: By changing its altitude, a stratospheric balloon can surf winds moving in different directions.

Original: BLE Evaluation .
Revised: BLE Evaluation .

Original: The goal of a BLE agent is to station-keep, i.e., to control a balloon to stay within 50 km of a ﬁxed ground station by changing its altitude to catch winds that it ﬁnds favorable.
Revised: The goal of a BLE agent is to station-keep, i.e., to control a balloon to stay within 50 km of a ﬁxed ground station by changing its altitude to catch winds that it ﬁnds favorable.

Original: We measure how successful an agent is at station-keeping by measuring the fraction of time the balloon is within the speciﬁed radius, denoted TWR50 ( i.e., the time within a radius of 50km).
Revised: We measure how successful an agent is at station-keeping by measuring the fraction of time the balloon is within the speciﬁed radius, denoted TWR50 ( i.e., the time within a radius of 50km).

Original: Environment Details .
Revised: Environment Details .

Original: The observation space in BLE is a 1099 dimensional array of continuous and boolean values.
Revised: The observation space in BLE is a 1099 dimensional array of continuous and boolean values.

Original: An agent in BLE can choose from three actions to control the balloon: move up, down, or stay in place.
Revised: An agent in BLE can choose from three actions to control the balloon: move up, down, or stay in place.

Original: The balloon can only move laterally by “surﬁng” the winds at its altitude; the winds change over time and vary as the balloon changes position and altitude
Revised: The balloon can only move laterally by “surﬁng” the winds at its altitude; the winds change over time and vary as the balloon changes position and altitude

Original: More details can be found at https://balloon-learning-environment.readthedocs.io/ en/latest/environment.html .
Revised: More details can be found at https://balloon-learning-environment.readthedocs.io/ en/latest/environment.html .

Original: Perciatelli Teacher and Data .
Revised: Perciatelli Teacher and Data .

Original: Perciatelli is the name of the RL agent (QR-DQN with a MLP architecture) trained by Bellemare et al.
Revised: Perciatelli is the name of the RL agent (QR-DQN with a MLP architecture) trained by Bellemare et al.

Original: [11] using a distributed RL setup for more than a month in the production-level Loon simulator and released with the BLE environment after ﬁne-tuning for 14M steps in BLE.
Revised: [11] using a distributed RL setup for more than a month in the production-level Loon simulator and released with the BLE environment after ﬁne-tuning for 14M steps in BLE.

Original: For the data, we use the ﬁnal replay buffer (of size 2M transitions) logged by the
Revised: For the data, we use the ﬁnal replay buffer (of size 2M transitions) logged by the

Original: Perciatelli agent during BLE ﬁne-tuning.
Revised: Perciatelli agent during BLE ﬁne-tuning.

Original: Architectures .
Revised: Architectures .

Original: The network architecture used by QR-DQN [23] and Perciatelli is a multilayer perceptron (MLP) with 7 hidden layers of size 600 each with ReLU activations and approximate the distribution using 51 ﬁxed quantiles.
Revised: The network architecture used by QR-DQN [23] and Perciatelli is a multilayer perceptron (MLP) with 7 hidden layers of size 600 each with ReLU activations and approximate the distribution using 51 ﬁxed quantiles.

Original: For the DenseNet architecture [39] employed by IQN [22] and
Revised: For the DenseNet architecture [39] employed by IQN [22] and

Original: R2D6, we use 7 hidden layers of size 512 each (for TPU-efﬁciency), which contains signiﬁcantly more parameters than the Perciatelli MLP.
Revised: R2D6, we use 7 hidden layers of size 512 each (for TPU-efﬁciency), which contains signiﬁcantly more parameters than the Perciatelli MLP.

Original: Additionally, R2D6 uses a LSTM layer of size 512 on top of the DenseNet encoder with QR-DQN loss, while IQN samples 128 quantiles for minimizing the implicit quantile regression loss.
Revised: Additionally, R2D6 uses a LSTM layer of size 512 on top of the DenseNet encoder with QR-DQN loss, while IQN samples 128 quantiles for minimizing the implicit quantile regression loss.

Original: Hyperparameters .
Revised: Hyperparameters .

Original: We set most hyperparameters for our distributed RL agents based on conﬁguration of the BLE Quantile agent, which can be found at agents/conﬁgs/quantile.gin.
Revised: We set most hyperparameters for our distributed RL agents based on conﬁguration of the BLE Quantile agent, which can be found at agents/conﬁgs/quantile.gin.

Original: For tabula rasa agents, we swept over the lr in { 2 e − 6 , 6 e − 6 , 1 e − 5 } and found 1 e − 5 to be the best performing lr .
Revised: For tabula rasa agents, we swept over the lr in { 2 e − 6 , 6 e − 6 , 1 e − 5 } and found 1 e − 5 to be the best performing lr .

Original: However, for ﬁne-tuning Perciatelli, we found that a lower lr of 1 e − 6 performs better.
Revised: However, for ﬁne-tuning Perciatelli, we found that a lower lr of 1 e − 6 performs better.

Original: For reincarnated R2D6 and IQN, we use a lr of 1 e − 5 and 6 e − 6 respectively during the online phase while 2 × lr in the ofﬂine pretraining phase.
Revised: For reincarnated R2D6 and IQN, we use a lr of 1 e − 5 and 6 e − 6 respectively during the online phase while 2 × lr in the ofﬂine pretraining phase.

Original: We set distillation temperature τ to be equal to 1 . 0 and linearly decay the QDagger distillation coefﬁcient λ t over a ﬁxed number of learner steps (1M for
Revised: We set distillation temperature τ to be equal to 1 . 0 and linearly decay the QDagger distillation coefﬁcient λ t over a ﬁxed number of learner steps (1M for

Original: R2D6 and 160000 for IQN).
Revised: R2D6 and 160000 for IQN).

Original: Furthermore, we swept over the initial value of λ t ( λ 0 ) in { 0 . 3 , 1 . 0 } and found 1.0 to be better for R2D6 while 0.3 for IQN.
Revised: Furthermore, we swept over the initial value of λ t ( λ 0 ) in { 0 . 3 , 1 . 0 } and found 1.0 to be better for R2D6 while 0.3 for IQN.

Original: A.5 Additional ablations for QDagger
Revised: A.5 Additional ablations for QDagger

Original: Dependence on ofﬂine replay data .
Revised: Dependence on ofﬂine replay data .

Original: In the PVRL setting on ALE, we assumed access to the last replay buffer (containing 1M transitions) of the teacher DQN (Adam) agent trained for 400M frames.
Revised: In the PVRL setting on ALE, we assumed access to the last replay buffer (containing 1M transitions) of the teacher DQN (Adam) agent trained for 400M frames.

Original: This assumption is aligned with maximally reusing existing computational work and often holds
Revised: This assumption is aligned with maximally reusing existing computational work and often holds

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: in practice as last replay buffer of RL agents is typically logged on disk in addition to their policy checkpoints.
Revised: in practice as last replay buffer of RL agents is typically logged on disk in addition to their policy checkpoints.

Original: However, it is possible that we only have access to the teacher policy.
Revised: However, it is possible that we only have access to the teacher policy.

Original: In this scenario, even if we don’t have access to the teacher’s replay buffer, we can generate data using the teacher policy during the online RL phase (this would cost environment samples) and use this teacher collected data for pretraining with QDagger loss (analogous to the behavior cloning phase in Dagger).
Revised: In this scenario, even if we don’t have access to the teacher’s replay buffer, we can generate data using the teacher policy during the online RL phase (this would cost environment samples) and use this teacher collected data for pretraining with QDagger loss (analogous to the behavior cloning phase in Dagger).

Original: To verify this empirically, we ran a QDagger ablation on 4 games where we do not assume access to the teacher’s replay buffer.
Revised: To verify this empirically, we ran a QDagger ablation on 4 games where we do not assume access to the teacher’s replay buffer.

Original: As shown in Figure A.19, we found that collecting the same amount of teacher data as the ofﬂine replay leads to comparable performance on 3/4 games (Asterix, Qbert,
Revised: As shown in Figure A.19, we found that collecting the same amount of teacher data as the ofﬂine replay leads to comparable performance on 3/4 games (Asterix, Qbert,

Original: Seaquest).
Revised: Seaquest).

Original: Somewhat surprisingly, collecting only 500K transitions from teacher results in comparable performance to using 1M transitions, except on Asterix where we see substantially lower performance.
Revised: Somewhat surprisingly, collecting only 500K transitions from teacher results in comparable performance to using 1M transitions, except on Asterix where we see substantially lower performance.

Original: The slightly better performance with ofﬂine replay could be related to its better diversity than teacher collected data.
Revised: The slightly better performance with ofﬂine replay could be related to its better diversity than teacher collected data.

Original: While we used (cid:15) -greedy exploration with the teacher policy, the ofﬂine replay data is collected using possibly diverse policies, as the teacher agent was continually updated during training.
Revised: While we used (cid:15) -greedy exploration with the teacher policy, the ofﬂine replay data is collected using possibly diverse policies, as the teacher agent was continually updated during training.

Original: Effect of QDagger loss in online phase .
Revised: Effect of QDagger loss in online phase .

Original: In this work, we use QDagger loss during both the ofﬂine pretraining and online RL phase (Equation 2).
Revised: In this work, we use QDagger loss during both the ofﬂine pretraining and online RL phase (Equation 2).

Original: To evaluate the beneﬁt of QDagger loss in the online phase on ALE, we ran an ablation on 4 games where we use standard Q-learning instead of QDagger loss during the online RL phase.
Revised: To evaluate the beneﬁt of QDagger loss in the online phase on ALE, we ran an ablation on 4 games where we use standard Q-learning instead of QDagger loss during the online RL phase.

Original: As shown in Figure A.20, we see that the online phase helps improve performance on some games ( e.g., Space Invaders, Asterix) while not having much effect on others.
Revised: As shown in Figure A.20, we see that the online phase helps improve performance on some games ( e.g., Space Invaders, Asterix) while not having much effect on others.

Original: The impact of the QDagger loss in the online phase also depends on the ofﬂine replay buffer size.
Revised: The impact of the QDagger loss in the online phase also depends on the ofﬂine replay buffer size.

Original: For example, on the more complex BLE domain, we only had access to a small amount of replay data relative to the training budget of the Perciatelli teacher.
Revised: For example, on the more complex BLE domain, we only had access to a small amount of replay data relative to the training budget of the Perciatelli teacher.

Original: With this teacher, using the QDagger loss only during the ofﬂine phase resulted in much lower performance than using QDagger for both ofﬂine and online phase.
Revised: With this teacher, using the QDagger loss only during the ofﬂine phase resulted in much lower performance than using QDagger for both ofﬂine and online phase.

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]