Original: B ENCHMARKS FOR D EEP O FF -P OLICY E VALUATION
Revised: B ENCHMARKS FOR D EEP O FF -P OLICY E VALUATION

Original: A BSTRACT
Revised: A BSTRACT

Original: Off-policy evaluation (OPE) holds the promise of being able to leverage large, ofﬂine datasets for both evaluating and selecting complex policies for decision making.
Revised: Off-policy evaluation (OPE) holds the promise of being able to leverage large, ofﬂine datasets for both evaluating and selecting complex policies for decision making.

Original: The ability to learn ofﬂine is particularly important in many real-world domains, such as in healthcare, recommender systems, or robotics, where online data collection is an expensive and potentially dangerous process.
Revised: The ability to learn ofﬂine is particularly important in many real-world domains, such as in healthcare, recommender systems, or robotics, where online data collection is an expensive and potentially dangerous process.

Original: Being able to accurately evaluate and select high-performing policies without requiring online interaction could yield signiﬁcant beneﬁts in safety, time, and cost for these applications.
Revised: Being able to accurately evaluate and select high-performing policies without requiring online interaction could yield signiﬁcant beneﬁts in safety, time, and cost for these applications.

Original: While many OPE methods have been proposed in recent years, comparing results between papers is difﬁcult because currently there is a lack of a comprehensive and uniﬁed benchmark, and measuring algorithmic progress has been challenging due to the lack of difﬁcult evaluation tasks.
Revised: While many OPE methods have been proposed in recent years, comparing results between papers is difﬁcult because currently there is a lack of a comprehensive and uniﬁed benchmark, and measuring algorithmic progress has been challenging due to the lack of difﬁcult evaluation tasks.

Original: In order to address this gap, we present a collection of policies that in conjunction with existing ofﬂine datasets can be used for benchmarking off-policy evaluation.
Revised: In order to address this gap, we present a collection of policies that in conjunction with existing ofﬂine datasets can be used for benchmarking off-policy evaluation.

Original: Our tasks include a range of challenging high-dimensional continuous control problems, with wide selections of datasets and policies for performing policy selection.
Revised: Our tasks include a range of challenging high-dimensional continuous control problems, with wide selections of datasets and policies for performing policy selection.

Original: The goal of our benchmark is to provide a standardized measure of progress that is motivated from a set of principles designed to challenge and test the limits of existing OPE methods.
Revised: The goal of our benchmark is to provide a standardized measure of progress that is motivated from a set of principles designed to challenge and test the limits of existing OPE methods.

Original: We perform an evaluation of state-of-the-art algorithms and provide open-source access to our data and code to foster future research in this area † .
Revised: We perform an evaluation of state-of-the-art algorithms and provide open-source access to our data and code to foster future research in this area † .

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Reinforcement learning algorithms can acquire effective policies for a wide range of problems through active online interaction, such as in robotics (Kober et al., 2013), board games and video games (Tesauro, 1995;
Revised: Reinforcement learning algorithms can acquire effective policies for a wide range of problems through active online interaction, such as in robotics (Kober et al., 2013), board games and video games (Tesauro, 1995;

Original: Mnih et al., 2013; Vinyals et al., 2019), and recommender systems (Aggarwal et al., 2016).
Revised: Mnih et al., 2013; Vinyals et al., 2019), and recommender systems (Aggarwal et al., 2016).

Original: However, this sort of active online interaction is often impractical for real-world problems, where active data collection can be costly (Li et al., 2010), dangerous (Hauskrecht & Fraser, 2000; Kendall et al., 2019), or time consuming (Gu et al., 2017).
Revised: However, this sort of active online interaction is often impractical for real-world problems, where active data collection can be costly (Li et al., 2010), dangerous (Hauskrecht & Fraser, 2000; Kendall et al., 2019), or time consuming (Gu et al., 2017).

Original: Batch (or ofﬂine) reinforcement learning, has been studied extensively in domains such as healthcare (Thapa et al., 2005; Raghu et al., 2018), recommender systems (Dudík et al., 2014;
Revised: Batch (or ofﬂine) reinforcement learning, has been studied extensively in domains such as healthcare (Thapa et al., 2005; Raghu et al., 2018), recommender systems (Dudík et al., 2014;

Original: Theocharous et al., 2015; Swaminathan et al., 2017), education (Mandel et al., 2014), and robotics (Kalashnikov et al., 2018).
Revised: Theocharous et al., 2015; Swaminathan et al., 2017), education (Mandel et al., 2014), and robotics (Kalashnikov et al., 2018).

Original: A major challenge with such methods is the off-policy evaluation (OPE) problem, where one must evaluate the expected performance of policies solely from ofﬂine data.
Revised: A major challenge with such methods is the off-policy evaluation (OPE) problem, where one must evaluate the expected performance of policies solely from ofﬂine data.

Original: This is critical for several reasons, including providing high-conﬁdence guarantees prior to deployment (Thomas et al., 2015), and performing policy improvement and model selection (Bottou et al., 2013; Doroudi et al., 2017).
Revised: This is critical for several reasons, including providing high-conﬁdence guarantees prior to deployment (Thomas et al., 2015), and performing policy improvement and model selection (Bottou et al., 2013; Doroudi et al., 2017).

Original: The goal of this paper is to provide a standardized benchmark for evaluating OPE methods.
Revised: The goal of this paper is to provide a standardized benchmark for evaluating OPE methods.

Original: Although considerable theoretical (Thomas & Brunskill, 2016; Swaminathan & Joachims, 2015; Jiang & Li, 2015; Wang et al., 2017; Yang et al., 2020) and practical progress (Gilotte et al., 2018; Nie et al., 2019; Kalashnikov et al., 2018) on OPE algorithms has been made in a range of different domains, there are few broadly accepted evaluation tasks that combine complex, high-dimensional problems commonly explored by modern deep reinforcement learning algorithms (Bellemare et al., 2013;
Revised: Although considerable theoretical (Thomas & Brunskill, 2016; Swaminathan & Joachims, 2015; Jiang & Li, 2015; Wang et al., 2017; Yang et al., 2020) and practical progress (Gilotte et al., 2018; Nie et al., 2019; Kalashnikov et al., 2018) on OPE algorithms has been made in a range of different domains, there are few broadly accepted evaluation tasks that combine complex, high-dimensional problems commonly explored by modern deep reinforcement learning algorithms (Bellemare et al., 2013;

Original: Brockman et al., 2016) with standardized evaluation protocols and metrics.
Revised: Brockman et al., 2016) with standardized evaluation protocols and metrics.

Original: Our goal is to provide a set of tasks with a range of difﬁculty, excercise a variety of design properties, and provide policies with different behavioral patterns in order to establish a standardized framework for comparing OPE algorithms.
Revised: Our goal is to provide a set of tasks with a range of difﬁculty, excercise a variety of design properties, and provide policies with different behavioral patterns in order to establish a standardized framework for comparing OPE algorithms.

Original: We put particular emphasis on large datasets, long-horizon tasks, and task complexity to facilitate the development of scalable algorithms that can solve high-dimensional problems.
Revised: We put particular emphasis on large datasets, long-horizon tasks, and task complexity to facilitate the development of scalable algorithms that can solve high-dimensional problems.

Original: Our primary contribution is the D eep
Revised: Our primary contribution is the D eep

Original: O ff-
Revised: O ff-

Original: P olicy E valuation (DOPE) benchmark.
Revised: P olicy E valuation (DOPE) benchmark.

Original: DOPE is designed to measure the performance of OPE methods by 1) evaluating on challenging control tasks with properties known to be difﬁcult for OPE methods, but which occur in real-world scenarios, 2) evaluating across a range of policies with different values, to directly measure performance on policy evaluation, ranking and selection, and 3) evaluating in ideal and adversarial settings in terms of dataset coverage and support.
Revised: DOPE is designed to measure the performance of OPE methods by 1) evaluating on challenging control tasks with properties known to be difﬁcult for OPE methods, but which occur in real-world scenarios, 2) evaluating across a range of policies with different values, to directly measure performance on policy evaluation, ranking and selection, and 3) evaluating in ideal and adversarial settings in terms of dataset coverage and support.

Original: These factors are independent of task difﬁculty, but are known to have a large impact on OPE performance.
Revised: These factors are independent of task difﬁculty, but are known to have a large impact on OPE performance.

Original: To achieve 1, we selected tasks on a set of design principles outlined in Section 3.1.
Revised: To achieve 1, we selected tasks on a set of design principles outlined in Section 3.1.

Original: To achieve 2, for each task we include 10 to 96 policies for evaluation and devise an evaluation protocol that measures policy evaluation, ranking, and selection as outlined in Section 3.2.
Revised: To achieve 2, for each task we include 10 to 96 policies for evaluation and devise an evaluation protocol that measures policy evaluation, ranking, and selection as outlined in Section 3.2.

Original: To achieve 3, we provide two domains with differing dataset coverage and support properties described in Section 4.
Revised: To achieve 3, we provide two domains with differing dataset coverage and support properties described in Section 4.

Original: Finally, to enable an easy-to-use research platform, we provide the datasets, target policies, evaluation API, as well as the recorded results of state-of-the-art algorithms (presented in Section 5) as open-source.
Revised: Finally, to enable an easy-to-use research platform, we provide the datasets, target policies, evaluation API, as well as the recorded results of state-of-the-art algorithms (presented in Section 5) as open-source.

Original:  B ACKGROUND
Revised:  B ACKGROUND

Original: the goal is to estimate the value of a single policy given only data.
Revised: the goal is to estimate the value of a single policy given only data.

Original: Ofﬂine Policy
Revised: Ofﬂine Policy

Original: Selection (bottom) is a closely related problem: given a set of N policies, attempt to pick the best given only data.
Revised: Selection (bottom) is a closely related problem: given a set of N policies, attempt to pick the best given only data.

Original: We brieﬂy review the off-policy evaluation (OPE) problem setting.
Revised: We brieﬂy review the off-policy evaluation (OPE) problem setting.

Original: We consider Markov decision processes (MDPs), deﬁned by a tuple ( S , A , T , R, ρ 0 , γ ) , with state space S , action space A , transition distribution T ( s (cid:48) | s, a ) , initial state distribution ρ 0 ( s ) , reward function R ( s, a ) and discount factor γ ∈ (0 , 1] .
Revised: We consider Markov decision processes (MDPs), deﬁned by a tuple ( S , A , T , R, ρ 0 , γ ) , with state space S , action space A , transition distribution T ( s (cid:48) | s, a ) , initial state distribution ρ 0 ( s ) , reward function R ( s, a ) and discount factor γ ∈ (0 , 1] .

Original: In reinforcement learning, we are typically concerned with optimizing or estimating the performance of a policy π ( a | s ) .
Revised: In reinforcement learning, we are typically concerned with optimizing or estimating the performance of a policy π ( a | s ) .

Original: The performance of a policy is commonly measured by the policy value V π , deﬁned as the expected sum of discounted rewards:
Revised: The performance of a policy is commonly measured by the policy value V π , deﬁned as the expected sum of discounted rewards:

Original: [Equation]
Revised: [Equation]

Original: If we have access to state and action samples collected from a policy π , then we can use the sample mean of observed returns to estimate the value function above.
Revised: If we have access to state and action samples collected from a policy π , then we can use the sample mean of observed returns to estimate the value function above.

Original: However, in off-policy evaluation we are typically interested in estimating the value of a policy when the data is collected from a separate behavior policy π B ( a | s ) .
Revised: However, in off-policy evaluation we are typically interested in estimating the value of a policy when the data is collected from a separate behavior policy π B ( a | s ) .

Original: This setting can arise, for example, when data is being generated online from another process, or in the purely ofﬂine case when we have a historical dataset.
Revised: This setting can arise, for example, when data is being generated online from another process, or in the purely ofﬂine case when we have a historical dataset.

Original: In this work we consider the latter, purely ofﬂine setting.
Revised: In this work we consider the latter, purely ofﬂine setting.

Original: The typical setup for this problem formulation is that we are provided with a discount γ , a dataset of trajectories collected from a behavior policy D
Revised: The typical setup for this problem formulation is that we are provided with a discount γ , a dataset of trajectories collected from a behavior policy D

Original: = { ( s 0 , a 0 , r 0 , s 1 , . . . ) } , and optionally the action probabilities for the behavior policy π B ( a t
Revised: = { ( s 0 , a 0 , r 0 , s 1 , . . . ) } , and optionally the action probabilities for the behavior policy π B ( a t

Original: | s t ) .
Revised: | s t ) .

Original: In many practical applications, logging action propensities is not possible, for example, when the behavior policy is a mix of ML and hard-coded business logic.
Revised: In many practical applications, logging action propensities is not possible, for example, when the behavior policy is a mix of ML and hard-coded business logic.

Original: For this reason, we focus on the setting without propensities to encourage future work on behavior-agnostic OPE methods.
Revised: For this reason, we focus on the setting without propensities to encourage future work on behavior-agnostic OPE methods.

Original: For the methods that require propensities, we estimate the propensities with behavior cloning.
Revised: For the methods that require propensities, we estimate the propensities with behavior cloning.

Original: The objective can take multiple ﬂavors, as shown in Fig.
Revised: The objective can take multiple ﬂavors, as shown in Fig.

Original: A common task in OPE is to estimate the performance, or value, of a policy π (which may not be the same as π B ) so that the estimated value is as close as possible to V π under a metric such as MSE or absolute error.
Revised: A common task in OPE is to estimate the performance, or value, of a policy π (which may not be the same as π B ) so that the estimated value is as close as possible to V π under a metric such as MSE or absolute error.

Original: A second task is to perform policy selection, where the goal is to select the best policy or set of policies out of a group of candidates.
Revised: A second task is to perform policy selection, where the goal is to select the best policy or set of policies out of a group of candidates.

Original: This setup corresponds to how OPE is commonly used in practice, which is to ﬁnd the best performing strategy out of a pool when online evaluation is too expensive to be feasible.
Revised: This setup corresponds to how OPE is commonly used in practice, which is to ﬁnd the best performing strategy out of a pool when online evaluation is too expensive to be feasible.

Original:  DOPE: D EEP O FF -P OLICY E VALUATION
Revised:  DOPE: D EEP O FF -P OLICY E VALUATION

Original: The goal of the Deep Off-Policy Evaluation (DOPE) benchmark is to provide tasks that are challenging and effective measures of progress for OPE methods, yet is easy to use in order to better facilitate research.
Revised: The goal of the Deep Off-Policy Evaluation (DOPE) benchmark is to provide tasks that are challenging and effective measures of progress for OPE methods, yet is easy to use in order to better facilitate research.

Original: Therefore, we design our benchmark around a set of properties which are known to be difﬁcult for existing OPE methods in order to gauge their shortcomings, and keep all tasks amenable to simulation in order for the benchmark to be accessible and easy to evaluate.
Revised: Therefore, we design our benchmark around a set of properties which are known to be difﬁcult for existing OPE methods in order to gauge their shortcomings, and keep all tasks amenable to simulation in order for the benchmark to be accessible and easy to evaluate.

Original: 3. T ASK P ROPERTIES
Revised: 3. T ASK P ROPERTIES

Original: We describe our motivating properties for selecting tasks for the benchmark as follows:
Revised: We describe our motivating properties for selecting tasks for the benchmark as follows:

Original: High Dimensional Spaces (H) High-dimensionality is a key-feature in many real-world domains where it is difﬁcult to perform feature engineering, such as in robotics, autonomous driving, and more.
Revised: High Dimensional Spaces (H) High-dimensionality is a key-feature in many real-world domains where it is difﬁcult to perform feature engineering, such as in robotics, autonomous driving, and more.

Original: In these problems, it becomes challenging to accurately estimate quantities such as the value function without the use of high-capacity models such a neural networks and large datasets with wide state coverage.
Revised: In these problems, it becomes challenging to accurately estimate quantities such as the value function without the use of high-capacity models such a neural networks and large datasets with wide state coverage.

Original: Our benchmark contains complex continuous-space tasks which exercise these challenges.
Revised: Our benchmark contains complex continuous-space tasks which exercise these challenges.

Original: Long Time-Horizon (L) Long time horizon tasks are known to present difﬁcult challenges for OPE algorithms.
Revised: Long Time-Horizon (L) Long time horizon tasks are known to present difﬁcult challenges for OPE algorithms.

Original: Some algorithms have difﬁculty doing credit assignment for these tasks.
Revised: Some algorithms have difﬁculty doing credit assignment for these tasks.

Original: This can be made worse as the state dimension or action dimension increases.
Revised: This can be made worse as the state dimension or action dimension increases.

Original: Sparse Rewards (R) Sparse reward tasks increase the difﬁculty of credit assignment and add exploration challenges, which may interact with data coverage in the ofﬂine setting.
Revised: Sparse Rewards (R) Sparse reward tasks increase the difﬁculty of credit assignment and add exploration challenges, which may interact with data coverage in the ofﬂine setting.

Original: We include a range robotics and navigation tasks which are difﬁcult to solve due to reward sparsity.
Revised: We include a range robotics and navigation tasks which are difﬁcult to solve due to reward sparsity.

Original: Temporally extended control (T)
Revised: Temporally extended control (T)

Original: The ability to make decisions hierarchically is major challenge in many reinforcement learning applications.
Revised: The ability to make decisions hierarchically is major challenge in many reinforcement learning applications.

Original: We include two navigation tasks which require high-level planning in addition to low-level control in order to simulate the difﬁculty in such problems.
Revised: We include two navigation tasks which require high-level planning in addition to low-level control in order to simulate the difﬁculty in such problems.

Original: 3. E VALUATION P ROTOCOL
Revised: 3. E VALUATION P ROTOCOL

Original: The goal of DOPE to provide metrics for policy ranking, evaluation and selection.
Revised: The goal of DOPE to provide metrics for policy ranking, evaluation and selection.

Original: Many existing OPE methods have only been evaluated on point estimates of value such as MSE, but policy selection is an important, practical use-case of OPE.
Revised: Many existing OPE methods have only been evaluated on point estimates of value such as MSE, but policy selection is an important, practical use-case of OPE.

Original: In order to explicitly measure the quality of using OPE for policy selection, we provide a set of policies with varying value, and devise two metrics that measure how well OPE methods can rank policies.
Revised: In order to explicitly measure the quality of using OPE for policy selection, we provide a set of policies with varying value, and devise two metrics that measure how well OPE methods can rank policies.

Original: For each task we include a dataset of logged experiences D , and a set of policies { π 1 , π 2 , ..., π N } with varying values.
Revised: For each task we include a dataset of logged experiences D , and a set of policies { π 1 , π 2 , ..., π N } with varying values.

Original: For each policy, OPE algorithms must use D to produce an estimate of the policy’s value.
Revised: For each policy, OPE algorithms must use D to produce an estimate of the policy’s value.

Original: For evaluation of these estimates, we provide "ground truth values" { V π 1 , V π 2 , ..., V π N } that are computed by running the policy for M ≥ 1000 episodes, where the exact value of M is given by the number of episodes needed to lower the error bar on the ground truth values to 0 .
Revised: For evaluation of these estimates, we provide "ground truth values" { V π 1 , V π 2 , ..., V π N } that are computed by running the policy for M ≥ 1000 episodes, where the exact value of M is given by the number of episodes needed to lower the error bar on the ground truth values to 0 .

Original: The estimated values are then compared to these ground truth values using three different metrics encompassing both policy evaluation and selection (illustrated in Figure 2; see Appendix A.1 for mathematical deﬁnitions).
Revised: The estimated values are then compared to these ground truth values using three different metrics encompassing both policy evaluation and selection (illustrated in Figure 2; see Appendix A.1 for mathematical deﬁnitions).

Original: Absolute Error
Revised: Absolute Error

Original: This metric measures estimate accuracy instead of its usefulness for ranking.
Revised: This metric measures estimate accuracy instead of its usefulness for ranking.

Original: Error is the most commonly used metric to assess performance of OPE algorithms.
Revised: Error is the most commonly used metric to assess performance of OPE algorithms.

Original: We opted to use absolute error instead of MSE to be robust to outliers.
Revised: We opted to use absolute error instead of MSE to be robust to outliers.

Original: Regret@k
Revised: Regret@k

Original: This metric measures how much worse the best policies identiﬁed by the estimates are than the best policy in the entire set.
Revised: This metric measures how much worse the best policies identiﬁed by the estimates are than the best policy in the entire set.

Original: It is computed by identifying the top-k policies according to the estimated returns.
Revised: It is computed by identifying the top-k policies according to the estimated returns.

Original: Regret@k is the difference between the actual expected return of the best policy in the entire set, and the actual value of the best policy in the top-k set.
Revised: Regret@k is the difference between the actual expected return of the best policy in the entire set, and the actual value of the best policy in the top-k set.

Original: Rank correlation This metric directly measures how well estimated values rank policies, by computing the correlation between ordinal rankings according by the OPE estimates and ordinal rankings according to the ground truth values.
Revised: Rank correlation This metric directly measures how well estimated values rank policies, by computing the correlation between ordinal rankings according by the OPE estimates and ordinal rankings according to the ground truth values.

Original:  D OMAINS
Revised:  D OMAINS

Original: DOPE contains two domains designed to provide a more comprehensive picture of how well OPE methods perform in different settings.
Revised: DOPE contains two domains designed to provide a more comprehensive picture of how well OPE methods perform in different settings.

Original: These two domains are constructed using two benchmarks previously proposed for ofﬂine reinforcement learning: RL Unplugged (Gulcehre et al., 2020) and
Revised: These two domains are constructed using two benchmarks previously proposed for ofﬂine reinforcement learning: RL Unplugged (Gulcehre et al., 2020) and

Original: D4RL (Fu et al., 2020), and reﬂect the challenges found within them.
Revised: D4RL (Fu et al., 2020), and reﬂect the challenges found within them.

Original: The DOPE RL Unplugged domain is constrained in two important ways: 1) the data is always generated using online RL training, ensuring there is adequate coverage of the state-action space, and 2) the policies are generated by applying ofﬂine RL algorithms to the same dataset we use for evaluation, ensuring that the behavior policy and evaluation policies induce similar state-action distributions.
Revised: The DOPE RL Unplugged domain is constrained in two important ways: 1) the data is always generated using online RL training, ensuring there is adequate coverage of the state-action space, and 2) the policies are generated by applying ofﬂine RL algorithms to the same dataset we use for evaluation, ensuring that the behavior policy and evaluation policies induce similar state-action distributions.

Original: Using it, we hope to understand how OPE methods work as task complexity increases from simple Cartpole tasks to controlling a Humanoid body while controlling for ideal data.
Revised: Using it, we hope to understand how OPE methods work as task complexity increases from simple Cartpole tasks to controlling a Humanoid body while controlling for ideal data.

Original: On the other hand, the DOPE D4RL domain has: 1) data from various sources (including random exploration, human teleoperation, and RL-trained policies with limited exploration), which results in varying levels of coverage of the state-action space, and 2) policies that are generated using online
Revised: On the other hand, the DOPE D4RL domain has: 1) data from various sources (including random exploration, human teleoperation, and RL-trained policies with limited exploration), which results in varying levels of coverage of the state-action space, and 2) policies that are generated using online

Original: RL algorithms, making it less likely that the behavior and evaluation policies share similar induced state-action distributions.
Revised: RL algorithms, making it less likely that the behavior and evaluation policies share similar induced state-action distributions.

Original: Both of these result in distribution shift which is known to be challenging for OPE methods, even in simple tasks.
Revised: Both of these result in distribution shift which is known to be challenging for OPE methods, even in simple tasks.

Original: So, using it we hope to measure how well OPE methods work in more practical data settings.
Revised: So, using it we hope to measure how well OPE methods work in more practical data settings.

Original: 4. DOPE RL U NPLUGGED
Revised: 4. DOPE RL U NPLUGGED

Original: DeepMind Control Suite (Tassa et al., 2018) is a set of control tasks implemented in MuJoCo (Todorov et al., 2012).
Revised: DeepMind Control Suite (Tassa et al., 2018) is a set of control tasks implemented in MuJoCo (Todorov et al., 2012).

Original: We consider the subset included in RL Unplugged.
Revised: We consider the subset included in RL Unplugged.

Original: This subset includes tasks that cover a range of difﬁculties.
Revised: This subset includes tasks that cover a range of difﬁculties.

Original: From Cartpole swingup, a simple task with a single degree of freedom, to Humanoid run which involves control of a complex bodies with 21 degrees of freedom.
Revised: From Cartpole swingup, a simple task with a single degree of freedom, to Humanoid run which involves control of a complex bodies with 21 degrees of freedom.

Original: All tasks use the default feature representation of the system state, including proprioceptive information such as joint positions and velocity, and additional sensor information and target position where appropriate.
Revised: All tasks use the default feature representation of the system state, including proprioceptive information such as joint positions and velocity, and additional sensor information and target position where appropriate.

Original: The observation dimension ranges from 5 to 67.
Revised: The observation dimension ranges from 5 to 67.

Original: Datasets and policies We train four ofﬂine RL algorithms (D4PG (Barth-Maron et al., 2018),
Revised: Datasets and policies We train four ofﬂine RL algorithms (D4PG (Barth-Maron et al., 2018),

Original: ABM (Siegel et al., 2020), CRR (Wang et al., 2020) and behavior cloning), varying their hyperparameters.
Revised: ABM (Siegel et al., 2020), CRR (Wang et al., 2020) and behavior cloning), varying their hyperparameters.

Original: For each algorithm-task-hyperparameter combination, we train an agent with 3 random seeds on the DM Control Suite dataset from RL Unplugged and record policy snapshots at exponentially increasing intervals (after 25k learner steps, 50k, 100K, 200K, etc).
Revised: For each algorithm-task-hyperparameter combination, we train an agent with 3 random seeds on the DM Control Suite dataset from RL Unplugged and record policy snapshots at exponentially increasing intervals (after 25k learner steps, 50k, 100K, 200K, etc).

Original: Following Gulcehre et al.
Revised: Following Gulcehre et al.

Original: (2020), we consider a deterministic policy for D4PG and stochastic policies for BC, ABM and CRR.
Revised: (2020), we consider a deterministic policy for D4PG and stochastic policies for BC, ABM and CRR.

Original: The datasets are taken from the RL Unplugged benchmark, where they were created by training multiple (online) RL agents and collecting both successful and unsuccessful episodes throughout training.
Revised: The datasets are taken from the RL Unplugged benchmark, where they were created by training multiple (online) RL agents and collecting both successful and unsuccessful episodes throughout training.

Original: All ofﬂine RL algorithms are implemented using the Acme framework (Hoffman et al., 2020).
Revised: All ofﬂine RL algorithms are implemented using the Acme framework (Hoffman et al., 2020).

Original: 4. DOPE D4RL
Revised: 4. DOPE D4RL

Original: Gym-MuJoCo tasks.
Revised: Gym-MuJoCo tasks.

Original: Gym-MuJoCo consists of several continuous control tasks implemented within the MuJoCo simulator (Todorov et al., 2012) and provided in the OpenAI Gym (Brockman et al., 2016) benchmark for online RL.
Revised: Gym-MuJoCo consists of several continuous control tasks implemented within the MuJoCo simulator (Todorov et al., 2012) and provided in the OpenAI Gym (Brockman et al., 2016) benchmark for online RL.

Original: We include the HalfCheetah, Hopper, Walker2D, and Ant tasks.
Revised: We include the HalfCheetah, Hopper, Walker2D, and Ant tasks.

Original: We include this domain primarily for comparison with past works, as a vast array of popular RL
Revised: We include this domain primarily for comparison with past works, as a vast array of popular RL

Original: [Table]
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: [Table]
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: methods have been evaluated and developed on these tasks (Schulman et al., 2015;
Revised: methods have been evaluated and developed on these tasks (Schulman et al., 2015;

Original: Lillicrap et al., 2015; Schulman et al., 2017; Fujimoto et al., 2018; Haarnoja et al., 2018).
Revised: Lillicrap et al., 2015; Schulman et al., 2017; Fujimoto et al., 2018; Haarnoja et al., 2018).

Original: Gym-MuJoCo datasets and policies.
Revised: Gym-MuJoCo datasets and policies.

Original: For each task, in order to explore the effect of varying distributions, we include 5 datasets originally proposed by Fu et al.
Revised: For each task, in order to explore the effect of varying distributions, we include 5 datasets originally proposed by Fu et al.

Original: 3 correspond to different performance levels of the agent – “random”, “medium”, and “expert”.
Revised: 3 correspond to different performance levels of the agent – “random”, “medium”, and “expert”.

Original: We additionally include a mixture of medium and expert dataset, labeled “medium-expert”, and data collected from a replay buffer until the policy reaches the medium level of performance, labeled “medium-replay”.
Revised: We additionally include a mixture of medium and expert dataset, labeled “medium-expert”, and data collected from a replay buffer until the policy reaches the medium level of performance, labeled “medium-replay”.

Original: For policies, we selected 11 policies collected from evenly-spaced snapshots of training a Soft Actor-Critic agent (Haarnoja et al., 2018), which covers a range of performance between random and expert.
Revised: For policies, we selected 11 policies collected from evenly-spaced snapshots of training a Soft Actor-Critic agent (Haarnoja et al., 2018), which covers a range of performance between random and expert.

Original: Maze2D and AntMaze tasks.
Revised: Maze2D and AntMaze tasks.

Original: Maze2D and AntMaze are two maze navigation tasks originally proposed in
Revised: Maze2D and AntMaze are two maze navigation tasks originally proposed in

Original: D4RL (Fu et al., 2020).
Revised: D4RL (Fu et al., 2020).

Original: The domain consists of 3 mazes ranging from easy to hard (“umaze”, “medium”, “large”), and two morphologies: a 2D ball in Maze2D and the “Ant” robot of the Gym benchmark in AntMaze.
Revised: The domain consists of 3 mazes ranging from easy to hard (“umaze”, “medium”, “large”), and two morphologies: a 2D ball in Maze2D and the “Ant” robot of the Gym benchmark in AntMaze.

Original: For Maze2D, we provide a less challenging reward computed base on distance to a ﬁxed goal.
Revised: For Maze2D, we provide a less challenging reward computed base on distance to a ﬁxed goal.

Original: For the AntMaze environment reward is given only upon reaching the ﬁxed goal.
Revised: For the AntMaze environment reward is given only upon reaching the ﬁxed goal.

Original: Maze2D and AntMaze datasets and policies.
Revised: Maze2D and AntMaze datasets and policies.

Original: Datasets for both morphologies consists of undirect data navigating randomly to different goal locations.
Revised: Datasets for both morphologies consists of undirect data navigating randomly to different goal locations.

Original: The datasets for Maze2D are collected by using a high-level planner to command waypoints to a low-level PID controller in order to reach randomly selected goals.
Revised: The datasets for Maze2D are collected by using a high-level planner to command waypoints to a low-level PID controller in order to reach randomly selected goals.

Original: The dataset in AntMaze is generated using the same high-level planner, but the low- level planner is replaced with a goal-conditioned policy trained to reach arbitrary waypoints.
Revised: The dataset in AntMaze is generated using the same high-level planner, but the low- level planner is replaced with a goal-conditioned policy trained to reach arbitrary waypoints.

Original: Both of these datasets are generated from non-Markovian policies, as the high-level controller maintains a history of waypoints reached in order to construct a plan to the goal.
Revised: Both of these datasets are generated from non-Markovian policies, as the high-level controller maintains a history of waypoints reached in order to construct a plan to the goal.

Original: We provide policies for all environments except “antmaze-large” by taking training snapshots obtained while running the DAPG algorithm (Rajeswaran et al., 2017).
Revised: We provide policies for all environments except “antmaze-large” by taking training snapshots obtained while running the DAPG algorithm (Rajeswaran et al., 2017).

Original: Because obtaining high-performing policies for “antmaze-large” was challenging, we instead used imitation learning on a large amount of expert data to generate evaluation policies.
Revised: Because obtaining high-performing policies for “antmaze-large” was challenging, we instead used imitation learning on a large amount of expert data to generate evaluation policies.

Original: This expert data is obtained by collecting additional trajectories that reach the goal using a high-level waypoint planner in conjunction with a low-level goal-conditioned policy (this is the same method as was used to generate the dataset, Sec. 5 (Fu et al., 2020)).
Revised: This expert data is obtained by collecting additional trajectories that reach the goal using a high-level waypoint planner in conjunction with a low-level goal-conditioned policy (this is the same method as was used to generate the dataset, Sec. 5 (Fu et al., 2020)).

Original: Adroit tasks.
Revised: Adroit tasks.

Original: The Adroit domain is a realistic simulation based on the
Revised: The Adroit domain is a realistic simulation based on the

Original: Shadow Hand robot, ﬁrst proposed by Rajeswaran et al.
Revised: Shadow Hand robot, ﬁrst proposed by Rajeswaran et al.

Original: There are 4 tasks in this domain: opening a door (“door”), pen twirling (“pen”), moving a ball to a target location (“relocate”), and hitting a nail with a hammer (“hammer”).
Revised: There are 4 tasks in this domain: opening a door (“door”), pen twirling (“pen”), moving a ball to a target location (“relocate”), and hitting a nail with a hammer (“hammer”).

Original: These tasks all contain sparse rewards and are difﬁcult to learn without demonstrations.
Revised: These tasks all contain sparse rewards and are difﬁcult to learn without demonstrations.

Original: Adroit datasets and policies.
Revised: Adroit datasets and policies.

Original: We include 3 datasets for each task.
Revised: We include 3 datasets for each task.

Original: The “human” dataset consists of a small amount of human demonstrations performing the task.
Revised: The “human” dataset consists of a small amount of human demonstrations performing the task.

Original: The “expert” dataset consists of data collected from an expert trained via
Revised: The “expert” dataset consists of data collected from an expert trained via

Original: DAPG (Rajeswaran et al., 2017).
Revised: DAPG (Rajeswaran et al., 2017).

Original: Finally, the “cloned” dataset contains a mixture of human demonstrations and data collected from an imitation learning algorithm trained on the demonstrations.
Revised: Finally, the “cloned” dataset contains a mixture of human demonstrations and data collected from an imitation learning algorithm trained on the demonstrations.

Original: For policies, we include 11 policies collected from snapshots while running the DAPG algorithm, which range from random performance to expert performance.
Revised: For policies, we include 11 policies collected from snapshots while running the DAPG algorithm, which range from random performance to expert performance.

Original:  B ASELINES AND R ESULTS
Revised:  B ASELINES AND R ESULTS

Original: The goal of our evaluation is two-fold.
Revised: The goal of our evaluation is two-fold.

Original: First, we wish to measure the performance of a variety of existing algorithms to provide baselines and reference numbers for future research.
Revised: First, we wish to measure the performance of a variety of existing algorithms to provide baselines and reference numbers for future research.

Original: Second, we wish to identify shortcomings in these approaches to reveal promising directions for future research.
Revised: Second, we wish to identify shortcomings in these approaches to reveal promising directions for future research.

Original: 5. B ASELINES
Revised: 5. B ASELINES

Original: We selected six methods to evaluate, which cover a variety of approaches that have been explored for the OPE problem.
Revised: We selected six methods to evaluate, which cover a variety of approaches that have been explored for the OPE problem.

Original: Fitted Q-Evaluation (FQE)
Revised: Fitted Q-Evaluation (FQE)

Original: As in Le et al.
Revised: As in Le et al.

Original: (2019), we train a neural network to estimate the value of the evaluation policy π by bootstrapping from Q ( s (cid:48) , π ( s (cid:48) )) .
Revised: (2019), we train a neural network to estimate the value of the evaluation policy π by bootstrapping from Q ( s (cid:48) , π ( s (cid:48) )) .

Original: We tried two different implementations, one from Kostrikov & Nachum (2020) 3 and another from Paine et al.
Revised: We tried two different implementations, one from Kostrikov & Nachum (2020) 3 and another from Paine et al.

Original: labeled FQE-L2 and
Revised: labeled FQE-L2 and

Original: FQE-D respectively to reﬂect different choices in loss function and parameterization.
Revised: FQE-D respectively to reﬂect different choices in loss function and parameterization.

Original: Model-Based (MB) Similar to Paduraru (2007), we train dynamics and reward models on transitions from the ofﬂine dataset D .
Revised: Model-Based (MB) Similar to Paduraru (2007), we train dynamics and reward models on transitions from the ofﬂine dataset D .

Original: Our models are deep neural networks trained to maximize the log likelihood of the next state and reward given the current state and action, similar to models from successful model-based RL algorithms (Chua et al., 2018; Janner et al., 2019).
Revised: Our models are deep neural networks trained to maximize the log likelihood of the next state and reward given the current state and action, similar to models from successful model-based RL algorithms (Chua et al., 2018; Janner et al., 2019).

Original: We follow the setup detailed in Zhang et al.
Revised: We follow the setup detailed in Zhang et al.

Original: We include both the feed-forward and auto-regressive models labeled
Revised: We include both the feed-forward and auto-regressive models labeled

Original: MB-FF and MB-AR
Revised: MB-FF and MB-AR

Original: respectively.
Revised: respectively.

Original: To evaluate a policy, we compute the return using simulated trajectories generated by the policy under the learned dynamics model.
Revised: To evaluate a policy, we compute the return using simulated trajectories generated by the policy under the learned dynamics model.

Original: Importance Sampling (IS)
Revised: Importance Sampling (IS)

Original: We perform importance sampling with a learned behavior policy.
Revised: We perform importance sampling with a learned behavior policy.

Original: We use the implementation from Kostrikov & Nachum (2020) 3 , which uses self-normalized (also known as weighted) step-wise importance sampling (Precup, 2000).
Revised: We use the implementation from Kostrikov & Nachum (2020) 3 , which uses self-normalized (also known as weighted) step-wise importance sampling (Precup, 2000).

Original: Since the behavior policy is not known explicitly, we learn an estimate of it via a max-likelihood objective over the dataset D , as advocated by Xie et al.
Revised: Since the behavior policy is not known explicitly, we learn an estimate of it via a max-likelihood objective over the dataset D , as advocated by Xie et al.

Original: ; Hanna et al.
Revised: ; Hanna et al.

Original: In order to be able to compute log-probabilities when the target policy is deterministic, we add artiﬁcial Gaussian noise with standard deviation 0 .
Revised: In order to be able to compute log-probabilities when the target policy is deterministic, we add artiﬁcial Gaussian noise with standard deviation 0 .

Original: 01 for all deterministic target policies.
Revised: 01 for all deterministic target policies.

Original: MB-AR FQE-D DR MB-FF FQE-L2 DICE IS VPM Baselines0.
Revised: MB-AR FQE-D DR MB-FF FQE-L2 DICE IS VPM Baselines0.

Original: <
Revised: <

Original: A b s o l u t e
Revised: A b s o l u t e

Original: E rr o r
Revised: E rr o r

Original: MB-AR FQE-D MB-FF FQE-L2 DR VPM IS DICE Baselines 0 0.
Revised: MB-AR FQE-D MB-FF FQE-L2 DR VPM IS DICE Baselines 0 0.

Original: > R a n k C o rr e l a t i o n
Revised: > R a n k C o rr e l a t i o n

Original: MB-AR FQE-D MB-FF FQE-L2 VPM DR DICE IS Baselines0.
Revised: MB-AR FQE-D MB-FF FQE-L2 VPM DR DICE IS Baselines0.

Original: < R e g r e t @
Revised: < R e g r e t @

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

Original: <
Revised: <

Original: A b s o l u t e
Revised: A b s o l u t e

Original: E rr o r
Revised: E rr o r

Original: IS
Revised: IS

Original: DR
Revised: DR

Original: FQE-L
Revised: FQE-L

Original: VPM
Revised: VPM

Original: DICE Baselines 0.10.1 0.
Revised: DICE Baselines 0.10.1 0.

Original: > R a n k C o rr e l a t i o n
Revised: > R a n k C o rr e l a t i o n

Original: FQE-L
Revised: FQE-L

Original: IS
Revised: IS

Original: DR
Revised: DR

Original: VPM
Revised: VPM

Original: DICE Baselines0.1 0.
Revised: DICE Baselines0.1 0.

Original: < R e g r e t @
Revised: < R e g r e t @

Original: Doubly-Robust (DR)
Revised: Doubly-Robust (DR)

Original: We perform weighted doubly-robust policy evaluation Thomas & Brunskill (2016) using the implementation of Kostrikov & Nachum (2020) 3 .
Revised: We perform weighted doubly-robust policy evaluation Thomas & Brunskill (2016) using the implementation of Kostrikov & Nachum (2020) 3 .

Original: Speciﬁcally, this method combines the IS technique above with a value estimator for variance reduction.
Revised: Speciﬁcally, this method combines the IS technique above with a value estimator for variance reduction.

Original: The value estimator is learned using deep FQE with an L2 loss function.
Revised: The value estimator is learned using deep FQE with an L2 loss function.

Original: More advanced approaches that trade variance for bias exist (e.g., MAGIC (Thomas & Brunskill, 2016)), but we leave implementing them to future work.
Revised: More advanced approaches that trade variance for bias exist (e.g., MAGIC (Thomas & Brunskill, 2016)), but we leave implementing them to future work.

Original: DICE This method uses a saddle-point objective to estimate marginalized importance weights
Revised: DICE This method uses a saddle-point objective to estimate marginalized importance weights

Original: d π ( s, a ) /d
Revised: d π ( s, a ) /d

Original: π B ( s, a ) ; these weights are then used to compute a weighted average of reward over the ofﬂine dataset, and this serves as an estimate of the policy’s value in the MDP.
Revised: π B ( s, a ) ; these weights are then used to compute a weighted average of reward over the ofﬂine dataset, and this serves as an estimate of the policy’s value in the MDP.

Original: We use the implementation from Yang et al.
Revised: We use the implementation from Yang et al.

Original: (2020) corresponding to the algorithm BestDICE .
Revised: (2020) corresponding to the algorithm BestDICE .

Original: Variational Power Method (VPM)
Revised: Variational Power Method (VPM)

Original: This method runs a variational power iteration algorithm to estimate the importance weights
Revised: This method runs a variational power iteration algorithm to estimate the importance weights

Original: d π ( s, a ) /d
Revised: d π ( s, a ) /d

Original: π B ( s, a ) without the knowledge of the behavior policy.
Revised: π B ( s, a ) without the knowledge of the behavior policy.

Original: It then estimates the target policy value using weighted average of rewards similar to the DICE method.
Revised: It then estimates the target policy value using weighted average of rewards similar to the DICE method.

Original: Our implementation is based on the same network and hyperparameters for OPE setting as in Wen et al.
Revised: Our implementation is based on the same network and hyperparameters for OPE setting as in Wen et al.

Original: We further tune the hyper-parameters including the regularization parameter λ , learning rates α θ
Revised: We further tune the hyper-parameters including the regularization parameter λ , learning rates α θ

Original: and α v , and number of iterations on the Cartpole swingup task using ground-truth policy value, and then ﬁx them for all other tasks.
Revised: and α v , and number of iterations on the Cartpole swingup task using ground-truth policy value, and then ﬁx them for all other tasks.

Original: 5. R ESULTS
Revised: 5. R ESULTS

Original: To facilitate aggregate metrics and comparisons between tasks and between DOPE RL Unplugged and DOPE D4RL, we normalize the returns and estimated returns to range between 0 and 1.
Revised: To facilitate aggregate metrics and comparisons between tasks and between DOPE RL Unplugged and DOPE D4RL, we normalize the returns and estimated returns to range between 0 and 1.

Original: For each set of policies we compute the worst value V worst =
Revised: For each set of policies we compute the worst value V worst =

Original: min { V π 1 , V π 2 , ..., V π N } and best value
Revised: min { V π 1 , V π 2 , ..., V π N } and best value

Original: V best = max { V π 1 , V π 2 , ..., V π N } and normalize the returns and estimated returns according to x (cid:48)
Revised: V best = max { V π 1 , V π 2 , ..., V π N } and normalize the returns and estimated returns according to x (cid:48)

Original: = ( x − V worst ) /
Revised: = ( x − V worst ) /

Original: ( V best − V worst ) .
Revised: ( V best − V worst ) .

Original: We present results averaged across DOPE RL Unplugged in Fig. 4, and results for DOPE D4RL in
Revised: We present results averaged across DOPE RL Unplugged in Fig. 4, and results for DOPE D4RL in

Original: Fig.
Revised: Fig.

Original: Overall, no evaluated algorithm attains near-oracle performance under any metric (absolute error, regret, or rank correlation).
Revised: Overall, no evaluated algorithm attains near-oracle performance under any metric (absolute error, regret, or rank correlation).

Original: Because the dataset is ﬁnite, we do not expect that achieving oracle performance is possible.
Revised: Because the dataset is ﬁnite, we do not expect that achieving oracle performance is possible.

Original: Nevertheless, based on recent progress on this benchmark (e.g., Zhang et al.
Revised: Nevertheless, based on recent progress on this benchmark (e.g., Zhang et al.

Original: (2021)), we hypothesize that the benchmark has room for improvement, making it suitable for driving further improvements on OPE methods and facilitating the development of OPE algorithms that can provide reliable estimates on the types of high-dimensional problems that we consider.
Revised: (2021)), we hypothesize that the benchmark has room for improvement, making it suitable for driving further improvements on OPE methods and facilitating the development of OPE algorithms that can provide reliable estimates on the types of high-dimensional problems that we consider.

Original: While all algorithms achieve sub-optimal performance, some perform better than others.
Revised: While all algorithms achieve sub-optimal performance, some perform better than others.

Original: We ﬁnd that on the DOPE RL Unplugged tasks model based (MB-AR, MB-FF) and direct value based methods (FQE-D, FQE-L2) signiﬁcantly outperform importance sampling methods (VPM, DICE, IS) across all metrics.
Revised: We ﬁnd that on the DOPE RL Unplugged tasks model based (MB-AR, MB-FF) and direct value based methods (FQE-D, FQE-L2) signiﬁcantly outperform importance sampling methods (VPM, DICE, IS) across all metrics.

Original: This is somewhat surprising as DICE and VPM have shown promising results in other settings.
Revised: This is somewhat surprising as DICE and VPM have shown promising results in other settings.

Original: We hypothesize that this is due to the relationship between the behavior data and evaluation policies, which is different from standard OPE settings.
Revised: We hypothesize that this is due to the relationship between the behavior data and evaluation policies, which is different from standard OPE settings.

Original: Recall that in DOPE RL Unplugged the behavior data is collected from an online RL algorithm and the evaluation policies are learned via ofﬂine RL from the behavior data.
Revised: Recall that in DOPE RL Unplugged the behavior data is collected from an online RL algorithm and the evaluation policies are learned via ofﬂine RL from the behavior data.

Original: In our experience all methods work better when the behavior policy is a noisy/perturbed version of the evaluation policy.
Revised: In our experience all methods work better when the behavior policy is a noisy/perturbed version of the evaluation policy.

Original: Moreover, MB and FQE-based methods may
Revised: Moreover, MB and FQE-based methods may

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

Original: implicitly beneﬁt from the architectural and optimization advancements made in policy optimization settings, which focus on similar environments and where these methods are more popular than importance sampling approaches.
Revised: implicitly beneﬁt from the architectural and optimization advancements made in policy optimization settings, which focus on similar environments and where these methods are more popular than importance sampling approaches.

Original: Note that within the MB and FQE methods, design details can create a signiﬁcant difference in performance.
Revised: Note that within the MB and FQE methods, design details can create a signiﬁcant difference in performance.

Original: For example model architecture (MB-AR vs MB-FF) and implementation differences (FQE-D vs FQE-L2) show differing performance on certain tasks.
Revised: For example model architecture (MB-AR vs MB-FF) and implementation differences (FQE-D vs FQE-L2) show differing performance on certain tasks.

Original: On DOPE D4RL, direct value based methods still do well, with FQE-L2 performing best on the
Revised: On DOPE D4RL, direct value based methods still do well, with FQE-L2 performing best on the

Original: Absolute Error and Regret@1 metrics.
Revised: Absolute Error and Regret@1 metrics.

Original: However, there are cases where other methods outperform
Revised: However, there are cases where other methods outperform

Original: FQE.
Revised: FQE.

Original: Notably, IS and DR outperform FQE-L2 under the rank correlation metric.
Revised: Notably, IS and DR outperform FQE-L2 under the rank correlation metric.

Original: As expected, there is a clear performance gap between DOPE RL Unplugged and DOPE D4RL.
Revised: As expected, there is a clear performance gap between DOPE RL Unplugged and DOPE D4RL.

Original: While both domains have challenging tasks, algorithms perform better under the more ideal conditions of DOPE RL Unplugged than under the challenging conditions of DOPE D4RL (0.69 vs 0.25 rank correlation respectively).
Revised: While both domains have challenging tasks, algorithms perform better under the more ideal conditions of DOPE RL Unplugged than under the challenging conditions of DOPE D4RL (0.69 vs 0.25 rank correlation respectively).

Original: In Fig.
Revised: In Fig.

Original: A.2 we show the rank correlation for each task in DOPE RL Unplugged.
Revised: A.2 we show the rank correlation for each task in DOPE RL Unplugged.

Original: Most tasks follow the overall trends, but we will highlight a few exceptions.
Revised: Most tasks follow the overall trends, but we will highlight a few exceptions.

Original: 1) Importance sampling is among the best methods for the humanoid run task, signiﬁcantly outperforming direct value-based methods. 2) while MB-AR and FQE-D are similar overall, there are a few tasks where the difference is large, for example FQE-D outperfroms MB-AR on ﬁnger turn hard , and manipulator insert ball , where as MB-AR outperforms FQE-D on cartpole swingup , ﬁsh swim , humanoid run , and manipulator insert peg .
Revised: 1) Importance sampling is among the best methods for the humanoid run task, signiﬁcantly outperforming direct value-based methods. 2) while MB-AR and FQE-D are similar overall, there are a few tasks where the difference is large, for example FQE-D outperfroms MB-AR on ﬁnger turn hard , and manipulator insert ball , where as MB-AR outperforms FQE-D on cartpole swingup , ﬁsh swim , humanoid run , and manipulator insert peg .

Original: We show the scatter plots for MB-AR and FQE-D on these tasks in Fig 7 which highlights different failure modes: when MB-AR performs worse, it assigns similar values for all policies; when
Revised: We show the scatter plots for MB-AR and FQE-D on these tasks in Fig 7 which highlights different failure modes: when MB-AR performs worse, it assigns similar values for all policies; when

Original: FQE-D performs worse, it severely over-estimates the values of poor policies.
Revised: FQE-D performs worse, it severely over-estimates the values of poor policies.

Original: We present more detailed results, separated by task, in Appendix A.2.
Revised: We present more detailed results, separated by task, in Appendix A.2.

Original: Note in particular how in
Revised: Note in particular how in

Original: Table A.2.2, which shows the regret@1 metric for different D4RL tasks, the particular choice of dataset for the Gym-MuJoCo, Adroit, and AntMaze domains causes a signiﬁcant difference in the performance of OPE methods.
Revised: Table A.2.2, which shows the regret@1 metric for different D4RL tasks, the particular choice of dataset for the Gym-MuJoCo, Adroit, and AntMaze domains causes a signiﬁcant difference in the performance of OPE methods.

Original: This indicates the importance of evaluating multiple distinct datasets, with different data distribution properties (e.g., more narrow datasets, such as expert data, vs. broader datasets, such as random data), as no tested method is reliably robust to the effects of dataset variation.
Revised: This indicates the importance of evaluating multiple distinct datasets, with different data distribution properties (e.g., more narrow datasets, such as expert data, vs. broader datasets, such as random data), as no tested method is reliably robust to the effects of dataset variation.

Original: High-dimensional tasks requiring temporally extended control were also challenging, as highlighted by the performance on the AntMaze domain.
Revised: High-dimensional tasks requiring temporally extended control were also challenging, as highlighted by the performance on the AntMaze domain.

Original: No algorithm was able to achieve a good absolute error value on such tasks, and importance sampling was the only method able to achieve a correlation consistently above zero, suggesting that these more complex tasks are a particularly important area for future methods to focus on.
Revised: No algorithm was able to achieve a good absolute error value on such tasks, and importance sampling was the only method able to achieve a correlation consistently above zero, suggesting that these more complex tasks are a particularly important area for future methods to focus on.

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: Off-policy evaluation (OPE) has been studied extensively across a range of different domains, from healthcare (Thapa et al., 2005; Raghu et al., 2018; Nie et al., 2019), to recommender systems (Li et al., 2010; Dudík et al., 2014; Theocharous et al., 2015), and robotics (Kalashnikov et al., 2018).
Revised: Off-policy evaluation (OPE) has been studied extensively across a range of different domains, from healthcare (Thapa et al., 2005; Raghu et al., 2018; Nie et al., 2019), to recommender systems (Li et al., 2010; Dudík et al., 2014; Theocharous et al., 2015), and robotics (Kalashnikov et al., 2018).

Original: While a full survey of OPE methods is outside the scope of this article, broadly speaking we can categories OPE methods into groups based the use of importance sampling (Precup, 2000), value functions (Sutton et al., 2009; Migliavacca et al., 2010; Sutton et al., 2016; Yang et al., 2020), and learned transition models (Paduraru, 2007), though a number of methods combine two or more of these components (Jiang & Li, 2015; Thomas & Brunskill, 2016; Munos et al., 2016).
Revised: While a full survey of OPE methods is outside the scope of this article, broadly speaking we can categories OPE methods into groups based the use of importance sampling (Precup, 2000), value functions (Sutton et al., 2009; Migliavacca et al., 2010; Sutton et al., 2016; Yang et al., 2020), and learned transition models (Paduraru, 2007), though a number of methods combine two or more of these components (Jiang & Li, 2015; Thomas & Brunskill, 2016; Munos et al., 2016).

Original: A signiﬁcant body of work in OPE is also concerned with providing statistical guarantees (Thomas et al., 2015).
Revised: A signiﬁcant body of work in OPE is also concerned with providing statistical guarantees (Thomas et al., 2015).

Original: Our focus instead is on empirical evaluation – while theoretical analysis is likely to be a critical part of future OPE research, combining such analysis with empirical demonstration on broadly accepted and standardized benchmarks is likely to facilitate progress toward practically useful algorithms.
Revised: Our focus instead is on empirical evaluation – while theoretical analysis is likely to be a critical part of future OPE research, combining such analysis with empirical demonstration on broadly accepted and standardized benchmarks is likely to facilitate progress toward practically useful algorithms.

Original: Current evaluation of OPE methods is based around several metrics, including error in predicting the true return of the evaluated policy (Voloshin et al., 2019), correlation between the evaluation output and actual returns (Irpan et al., 2019), and ranking and model selection metrics (Doroudi et al., 2017).
Revised: Current evaluation of OPE methods is based around several metrics, including error in predicting the true return of the evaluated policy (Voloshin et al., 2019), correlation between the evaluation output and actual returns (Irpan et al., 2019), and ranking and model selection metrics (Doroudi et al., 2017).

Original: As there is no single accepted metric used by the entire community, we provide a set of candidate metrics along with our benchmark, with a detailed justiﬁcation in Section 5.
Revised: As there is no single accepted metric used by the entire community, we provide a set of candidate metrics along with our benchmark, with a detailed justiﬁcation in Section 5.

Original: Our work is closely related to (Paine et al., 2020) which studies OPE in a similar setting, however in our work we present a benchmark for the community and compare a range of OPE methods.
Revised: Our work is closely related to (Paine et al., 2020) which studies OPE in a similar setting, however in our work we present a benchmark for the community and compare a range of OPE methods.

Original: Outside of OPE, standardized benchmark suites have led to considerable standardization and progress in RL (Stone & Sutton, 2001;
Revised: Outside of OPE, standardized benchmark suites have led to considerable standardization and progress in RL (Stone & Sutton, 2001;

Original: Dutech et al., 2005; Riedmiller et al., 2007).
Revised: Dutech et al., 2005; Riedmiller et al., 2007).

Original: The Arcade Learning Environment (ALE) (Bellemare et al., 2013) and OpenAI Gym (Brockman et al., 2016) have been widely used to compare online RL algorithms to good effect.
Revised: The Arcade Learning Environment (ALE) (Bellemare et al., 2013) and OpenAI Gym (Brockman et al., 2016) have been widely used to compare online RL algorithms to good effect.

Original: More recently, Gulcehre et al.
Revised: More recently, Gulcehre et al.

Original: Fu et al.
Revised: Fu et al.

Original: (2020) proposed benchmark tasks for ofﬂine RL.
Revised: (2020) proposed benchmark tasks for ofﬂine RL.

Original: Our benchmark is based on the tasks and environments described in these two benchmarks, which we augment with a set of standardized policies for evaluation, results for a number of existing OPE methods, and standardized evaluation metrics and protocols.
Revised: Our benchmark is based on the tasks and environments described in these two benchmarks, which we augment with a set of standardized policies for evaluation, results for a number of existing OPE methods, and standardized evaluation metrics and protocols.

Original: Voloshin et al.
Revised: Voloshin et al.

Original: (2019) have recently proposed benchmarking for OPE methods on a variety of tasks ranging from tabular problems to image-based tasks in Atari.
Revised: (2019) have recently proposed benchmarking for OPE methods on a variety of tasks ranging from tabular problems to image-based tasks in Atari.

Original: Our work differs in several key aspects.
Revised: Our work differs in several key aspects.

Original: Voloshin et al.
Revised: Voloshin et al.

Original: (2019) is composed entirely of discrete action tasks, whereas out benchmark focuses on continuous action tasks.
Revised: (2019) is composed entirely of discrete action tasks, whereas out benchmark focuses on continuous action tasks.

Original: Voloshin et al.
Revised: Voloshin et al.

Original: (2019) assumes full support for the evaluation policy under the behavior policy data, whereas we designed our datasets and policies to ensure that different cases of dataset and policy distributions could be studied.
Revised: (2019) assumes full support for the evaluation policy under the behavior policy data, whereas we designed our datasets and policies to ensure that different cases of dataset and policy distributions could be studied.

Original: Finally, all evaluations in Voloshin et al.
Revised: Finally, all evaluations in Voloshin et al.

Original: (2019) are performed using the MSE metric, and they do not provide standardized datasets.
Revised: (2019) are performed using the MSE metric, and they do not provide standardized datasets.

Original: In contrast, we provide a variety of policies for each problem which enables one to evaluate metrics such as ranking for policy selection, and a wide range of standardized datasets for reproducbility.
Revised: In contrast, we provide a variety of policies for each problem which enables one to evaluate metrics such as ranking for policy selection, and a wide range of standardized datasets for reproducbility.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: We have presented the Deep Off-Policy Evaluation (DOPE) benchmark, which aims to provide a platform for studying policy evaluation and selection across a wide range of challenging tasks and datasets.
Revised: We have presented the Deep Off-Policy Evaluation (DOPE) benchmark, which aims to provide a platform for studying policy evaluation and selection across a wide range of challenging tasks and datasets.

Original: In contrast to prior benchmarks, DOPE provides multiple datasets and policies, allowing researchers to study how data distributions affect performance and to evaluate a wide variety of metrics, including those that are relevant for ofﬂine policy selection.
Revised: In contrast to prior benchmarks, DOPE provides multiple datasets and policies, allowing researchers to study how data distributions affect performance and to evaluate a wide variety of metrics, including those that are relevant for ofﬂine policy selection.

Original: In comparing existing OPE methods, we ﬁnd that no existing algorithms consistently perform well across all of the tasks, which further reinforces the importance of standardized and challenging OPE benchmarks.
Revised: In comparing existing OPE methods, we ﬁnd that no existing algorithms consistently perform well across all of the tasks, which further reinforces the importance of standardized and challenging OPE benchmarks.

Original: Moreover, algorithms that perform poorly under one metric, such as absolute error, may perform better on other metrics, such as correlation, which provides insight into what algorithms to use depending on the use case (e.g., policy evaluation vs. policy selection).
Revised: Moreover, algorithms that perform poorly under one metric, such as absolute error, may perform better on other metrics, such as correlation, which provides insight into what algorithms to use depending on the use case (e.g., policy evaluation vs. policy selection).

Original: We believe that OPE is an exciting area for future research, as it allows RL agents to learn from large and abundant datasets in domains where online RL methods are otherwise infeasible.
Revised: We believe that OPE is an exciting area for future research, as it allows RL agents to learn from large and abundant datasets in domains where online RL methods are otherwise infeasible.

Original: We hope that our benchmark will enable further progress in this ﬁeld, though important evaluation challenges remain.
Revised: We hope that our benchmark will enable further progress in this ﬁeld, though important evaluation challenges remain.

Original: As the key beneﬁt of OPE is the ability to utilize real-world datasets, a promising direction for future evaluation efforts is to devise effective ways to use such data, where a key challenge is to develop evaluation protocols that are both reproducible and accessible.
Revised: As the key beneﬁt of OPE is the ability to utilize real-world datasets, a promising direction for future evaluation efforts is to devise effective ways to use such data, where a key challenge is to develop evaluation protocols that are both reproducible and accessible.

Original: This could help pave the way towards developing intelligent decision making agents that can leverage vast banks of logged information to solve important real-world problems.
Revised: This could help pave the way towards developing intelligent decision making agents that can leverage vast banks of logged information to solve important real-world problems.

Original: A A PPENDIX A. M ETRICS
Revised: A A PPENDIX A. M ETRICS

Original: The metrics we use in our paper are deﬁned as follows:
Revised: The metrics we use in our paper are deﬁned as follows:

Original: Absolute Error We evaluate policies using absolute error in order to be robust to outliers.
Revised: Absolute Error We evaluate policies using absolute error in order to be robust to outliers.

Original: The absolute error is deﬁned as the difference between the value and estimated value of a policy:
Revised: The absolute error is deﬁned as the difference between the value and estimated value of a policy:

Original: [Equation]
Revised: [Equation]

Original: Where V π is the true value of the policy, and ˆ V π is the estimated value of the policy.
Revised: Where V π is the true value of the policy, and ˆ V π is the estimated value of the policy.

Original: Regret@k Regret@k is the difference between the value of the best policy in the entire set, and the value of the best policy in the top-k set (where the top-k set is chosen by estimated values).
Revised: Regret@k Regret@k is the difference between the value of the best policy in the entire set, and the value of the best policy in the top-k set (where the top-k set is chosen by estimated values).

Original: It can be deﬁned as:
Revised: It can be deﬁned as:

Original: [Equation]
Revised: [Equation]

Original: Where topk (1 : N ) denotes the indices of the top K policies as measured by estimated values ˆ V π .
Revised: Where topk (1 : N ) denotes the indices of the top K policies as measured by estimated values ˆ V π .

Original: Rank correlation Rank correlation (also Spearman’s ρ ) measures the correlation between the ordinal rankings of the value estimates and the true values.
Revised: Rank correlation Rank correlation (also Spearman’s ρ ) measures the correlation between the ordinal rankings of the value estimates and the true values.

Original: It can be written as:
Revised: It can be written as:

Original: [Equation]
Revised: [Equation]

Original: A. D ETAILED R ESULTS
Revised: A. D ETAILED R ESULTS

Original: Detailed results ﬁgures and tables are presented here.
Revised: Detailed results ﬁgures and tables are presented here.

Original: We show results by task in both tabular and chart form, as well as scatter plots which compare the estimated returns against the ground truth returns for every policy.
Revised: We show results by task in both tabular and chart form, as well as scatter plots which compare the estimated returns against the ground truth returns for every policy.

Original: A.2. C HART R ESULTS
Revised: A.2. C HART R ESULTS

Original: First we show the normalized results for each algorithm and task.
Revised: First we show the normalized results for each algorithm and task.

Original: [Figure]
Revised: [Figure]

Original: VPM

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

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

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

Original: A.2. T ABULAR R ESULTS
Revised: T ABULAR R ESULTS

Original: Next, we present the results for each task and algorithm in tabular form, with means and standard deviations reported across 3 seeds.
Revised: Next, we present the results for each task and algorithm in tabular form, with means and standard deviations reported across 3 seeds

Revised: [Figure]

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

Revised: Autoregressive Model

Original: [Table]
Revised: [Table]

Revised: Also see Table A.3 and Table

Revised: .1 for

Revised: @5 and

Original: [Table]
Revised: [Table]

Original:  [Table]
Revised: R e g r e t @ 5 f o r O P E v s . g r ound [Table]

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

Original: [Figure]
Revised: [Figure]

Original: Finally, we present scatter plots plotting the true returns of each policy against the estimated returns.
Revised: Finally, we present scatter plots plotting the true returns of each policy against the estimated returns.

Original: Each point on the plot represents one evaluated policy.
Revised: Each point on the plot represents one evaluated policy

Original: [Figure]
Revised: [Figure]

Original: c a r t
Revised: VPM IS

Original: [Figure]
Revised: [Figure]

Original:  l 
Revised: c a r t p o l e

Original: [Figure]
Revised: [Figure]

Original: i 
Revised: i n g u p

Original: [Figure]
Revised: [Figure]

Original: t a h r un
Revised: t a h r un

Original: [Figure]
Revised: [Figure]

Original: i n g e r t u r n h a r d
Revised: i n g e r t u r n h a r d

Original: [Figure]
Revised: [Figure]

Original: f i s h s w i m
Revised: f i s h s w i m

Original: [Figure]
Revised: [Figure]

Original: hu
Revised: hu

Original: m a n o i d r un
Revised: m a n o i d r un

Original: [Figure]
Revised: [Figure]

Original: m a n i p u l a t
Revised: m a n i p u l a t

Original: o r i n s e r t b a ll
Revised: o r i n s e r t b a ll

Original: [Figure]
Revised: [Figure]

Original: m a n i p u l a t
Revised: m a n i p u l a t

Original: o r i n s e r t p e g
Revised: o r i n s e r t p e g

Original: [Figure]
Revised: [Figure]

Original: w a l k e r s t a n d
Revised: a l k e r s t a n d

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

Original: DR
Revised: DR

Original: FQE-L
Revised: FQE-L

Original: VPM
Revised: VPM

Original: DICE a n t e x p e r t
Revised: DICE a n t e x p e r t

Original: [Figure]
Revised: [Figure]

Original: a n t m e d i u m
Revised: a n t m e d i u m

Original: [Figure]
Revised: [Figure]

Original: a n t m e d i u m e x p e r t
Revised: a n t m e d i u m e x p e r t

Original: [Figure]
Revised: [Figure]

Original: a n t m e d i u m r e p l a y
Revised: a n t m e d i u m r e p l a y

Original: [Figure]
Revised: [Figure]

Original: a n t r a n d
Revised: a n t r a n d

Original: [Figure]
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Original: m
Revised: m

Original: [Figure]
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Original: n
Revised: n

Original: [Figure]
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Original: m a z e l a r
Revised: a z e l a r

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Revised: [Figure]

Original: i
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Original: [Figure]
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Original: e r
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Original: a n t m a z e l a r g e p l a y
Revised: a n t m a z e l a r g e p l a y

Original: [Figure]
Revised: [Figure]

Original: t i m a t
Revised: t i m a t

Original: [Figure]
Revised: [Figure]

Original: DR
Revised: DR

Original: FQE
Revised: FQE

Original: [Figure]
Revised: [Figure]

Original: L
Revised: L

Original: VPM
Revised: VPM

Original: DICE a n t m a z e m e d i u m d i v e r s e
Revised: DICE a n t m a z e m e d i u m d i v e r s e

Original: [Figure]
Revised: [Figure]

Original: a n t m a z e m e d i u m p l a y
Revised: a n t m a z e m e d i u m p l a y

Original: [Figure]
Revised: [Figure]

Original: a n
Revised: a n

Original: [Figure]
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Original: m a z e u m a
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Original: e
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Original: [Figure]
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Original: m a z e
Revised: m a z e

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Original: m a
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Original: e
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Original: i v e r
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Original: t
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Original: [Figure]
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Original: a t
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Original: [Figure]
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Original: FQE
Revised: FQE

Original: [Figure]
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Original: L
Revised: L

Original: VPM
Revised: VPM

Original: DICE h a l f c h ee t a h e x p e r t
Revised: DICE h a l f c h ee t a h e x p e r t

Original: [Figure]
Revised: [Figure]

Original: h a l f c h ee t a h m e d i u m
Revised: h a l f c h ee t a h m e d i u m

Original: [Figure]
Revised: [Figure]

Original: h a l f c h ee t a h m e d i u m e x p e r t
Revised: h a l f c h ee t a h m e d i u m e x p e r t

Original: [Figure]
Revised: [Figure]

Original: h a l f c h ee t a h m e d i u m r e p l a y
Revised: h a l f c h ee t a h m e d i u m r e p l a y

Original: [Figure]
Revised: [Figure]

Original: a l
Revised: a l

Original: [Figure]
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Original: c h ee t a h r a n d
Revised: c h ee t a h r a n d

Original: [Figure]
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Original: m
Revised: m

Original: [Figure]
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Original: r c l o n e
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Original: [Figure] [Figure]
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Original: m
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Original: [Figure]
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Original: FQE
Revised: FQE

Original: [Figure]
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Original: L
Revised: L

Original: [Figure]
Revised: VPM

Original: DICE h a mm e r hu
Revised: DICE h a mm e r hu

Original: m a n
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Original: [Figure]
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Original: h o pp e
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Original: r e x p e r t
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Original: h o pp e r m e d i u m
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Original: [Figure]
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Original: o pp e r r a n d o m
Revised: o pp e r r a n d o m

Original: [Figure]
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Original: m a z e 2 d u m a z e
Revised: m a z e 2 d u m a z e

Original: [Figure]
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Original: DR
Revised: DR

Original: FQE-L
Revised: FQE-L

Original: VPM
Revised: VPM

Original: DICE p e n c l o n e d
Revised: DICE p e n c l o n e d

Original: [Figure]
Revised: [Figure]

Original: p e n e x p e r t
Revised: p e n e x p e r t

Original: [Figure]
Revised: [Figure]

Original: p e n hu m a n
Revised: p e n hu m a n

Original: [Figure]
Revised: [Figure]

Original: r
Revised: r

Original: [Figure]
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Original: l o c a t e c l o n e
Revised: l o c a t e c l o n e

Original: [Figure]
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Original: r e l o c a t e e x p e r t
Revised: r e l o c a t e e x p e r t

Original: [Figure]
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Original: l
Revised: l

Original: [Figure]
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Original: c a t e
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Original: [Figure]
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Original: a n
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Original: [Figure]
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Original: w a l k e r 2 d e x p e r t
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Original: [Figure]
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Original: i
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Original: [Figure]
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Original: a
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Original: [Figure]
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Original: IS
Revised: IS

Original: [Figure]
Revised: [Figure]

Original: VPM
Revised: VPM

Original: DICE w a l k e r 2 d m e d i u m
Revised: DICE w a l k e r 2 d m e d i u m

Original: [Figure]
Revised: [Figure]

Original: w a l k e r 2 d m e d i u m e x p e r t
Revised: w a l k e r 2 d m e d i u m e x p e r t

Original: [Figure]
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Original:  k e r
Revised: l k e r

Original: [Figure]
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Original:  e d i u 
Revised: m e d i u m

Original: [Figure]
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Original: e p l a y
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Original: [Figure]
Revised: [Figure]