S EQUENCE - LEVEL I NTRINSIC E XPLORATION M ODEL FOR P ARTIALLY O BSERVABLE D OMAINS
Anonymous authors
Paper under double-blind review
A BSTRACT
Training reinforcement learning policies in partially observable domains with sparse reward signal is an important and open problem for the research community.
In this paper we introduce a new sequence-level intrinsic novelty model to tackle the challenge of training reinforcement learning policies in sparse rewarded partially observable domains.
First, we propose a new reasoning paradigm to infer the novelty for the partially observable states, which is built upon forward dynamics prediction.
Different from conventional approaches that perform self-prediction or one-step forward prediction, our proposed approach engages open-loop multi-step prediction, which enables the difﬁculty of novelty prediction to ﬂexibly scale and thus results in high-quality novelty scores.
Second, we propose a novel dual-LSTM architecture to facilitate the sequence-level reasoning over the partially observable state space.
Our proposed architecture efﬁciently synthesizes information from an observation sequence and an action sequence to derive meaningful latent representations for inferring the novelty for states.
To evaluate the efﬁciency of our proposed approach, we conduct extensive experiments on several challenging 3D navigation tasks from ViZDoom and DeepMind Lab .
We also present results on two hard-exploration domains from Atari 2600 series in Appendix to demonstrate our proposed approach could generalize beyond partially observable navigation tasks.
Overall, the experiment results reveal that our proposed intrinsic novelty model could outperform several state-of-the-art curiosity baselines with considerable signiﬁcance in the testiﬁed domains
I NTRODUCTION
Under the reinforcement learning formalism, the learning behavior of an agent is driven by the reward that the agent collects from the environment (Sutton and Barto, 1998).
However, many real-world problems have sparse rewards and most existing algorithms struggle with such sparsity.
One inherent reason that leads to the inferior performance of the conventional approaches in sparse reward domains is that initially, the agent trained with those approaches could hardly stumble into a reward/goal state by chance due to their simple exploration strategies (Pathak et al. , 2017).
To tackle the sparse reward problems, it is crucial to incentivize the agent’s exploration behavior.
One prominent line of solutions for encouraging agent’s exploration is via reward shaping (Singh, 1992; Dorigo and Colombetti, 1994), where the agent develops internal reward models to assign additional reward signals apart from the environment reward to encourage exploration.
To model the internal reward signal, often, the agent’s curiosity-driven behaviors are formalized as intrinsic novelty models (Schmidhuber, 1991; Singh et al. , 2004; Oudeyer et al. , 2007), which characterize agent’s experience to compute the novelty scores.
Our work belongs to the broad category of methods that solve the sparse reward problems with novelty models and reward shaping.
Speciﬁcally, we consider the line of sparse reward problems that employ partially observable inputs, with the inputs scaling to high-dimensional state spaces, such as images.
Such problems cover a range of important applications among AI research, e.g., navigation, robotics control and video game playing.
Even though the recently emerged intrinsic novelty models have demonstrate considerable efﬁciency in solving sparse reward problems with partial observability, we still face the following two major challenges.
First, inferring the novelty for the true state given only the partial observations still remains an open problem.
Most of today’s
[Figure]
state-of-the-art novelty models (e.g., (Savinov et al. , 2019; Pathak et al. , 2017)) only derive the novelty from local information, e.g., concatenation of few recent frames.
Second, though prediction error has been widely adopted as an effective metric to infer novelty, most of the existing approaches develop novelty model upon short-term prediction error such as 1-step look-ahead.
Such short-term prediction task might be an inadequate proxy for representing the novelty over state space, i.e., it might be too simple and thus result in inferior novelty scores.
Our key motivations are as follows.
First, sequence-level novelty models are desired to reason over the partially observable states with greater efﬁciency.
Second, the novelty model should consider longer-term prediction than self-prediction or 1-step look-ahead, to infer more meaningful novelty scores.
Based on the above intuitions, this work proposes a new sequence-level novelty model for partially observable domains with the following two distinct properties.
First, we introduce a dual-LSTM architecture to reason over a sequence of past transitions to construct the novelty model.
Second, we infer the novelty of a state from the prediction error of open-loop multi-step forward dynamics prediction, which is crucial to derive high quality novelty scores.
M ETHODOLOGY
Partially Observable Markov Decision Process (POMDP) generalizes MDPs by learning under partial observability.
Formally, a POMDP is deﬁned as a tuple (cid:104)S , A , O , T , Z , R(cid:105) , where S , A and O are the spaces for the state, action and observation, respectively.
The transition function
T ( s, a, s (cid:48) )
= p ( s (cid:48) | s, a ) speciﬁes the probability for transiting to state s (cid:48) after taking action a at state s .
The observation function Z ( s, a, o )
= p ( o | s, a ) deﬁnes the probability of receiving observation o after taking action a at state s .
The reward function R ( s, a ) deﬁnes the real-valued environment reward issued to the agent after taking action a at state s .
Under partial observability, the state space S is not accessible by the agent.
Thus, the agent performs decision making by forming a belief state b t from its observation space O , which integrates the information from the entire past history, i.e., ( o 0 , a 0 , o 1 , a 1 , ..., o t , a t ) .
The goal of reinforcement learning is to optimize a policy π ( b t ) that outputs an action distribution given each belief state b t , with the objective of maximizing the discounted cumulative rewards collected from each episode, i.e., (cid:80) ∞ t =
γ t r t , where γ ∈ (0 , 1] is a real-valued discount factor.
2. I NTRINSIC E XPLORATION F RAMEWORK
We now describe our proposed sequence-level intrinsic novelty model for partially observable domains with high-dimensional inputs (i.e., images).
Our primary focuses are the tasks where the external rewards r t are sparse, i.e., zero for most of the times.
This motivates us to engage a novelty function to infer the novelty over the state space and assign reward bonus to encourage exploration.
The novelty function is derived from a forward-inverse dynamics model.
Figure 1 depicts a high-level overview of our proposed sequence-level novelty computation.
To infer the novelty of a state at time t , we perform reasoning over a sequence of transitions with length L + H .
Intuitively, we use a sequence of H consequent observation frames together with a sequence of actions with length
L which are taken following the observation sequence, to predict the forward dynamics.
As such, the novelty model performs open-loop multi-step forward prediction.
By setting the length of the
[Figure]
Forward model   −
LSTM   −  −  +   −    −  − ( ,...,
)  ̂  −  −  +
̂  −  −1 LSTM
LSTM . . .
ℎ  ⊙ ⊖  +  . . .
ℎ
LSTM LSTM
LSTM
Inverse model   −  +   − ℎ  . . .
∗
LSTM   −  −  +  action sequence, i.e., L , our proposed paradigm could lead to forward dynamics prediction tasks with varying difﬁculty.
To process the input sequences, we propose a dual-LSTM architecture as shown in Figure 2.
Overall, each raw observation and action data are ﬁrst projected by their corresponding embedding modules.
Then LSTM modules are adopted over the sequences of observation/action embeddings to derive the sequential observation/action features.
Then the sequential observation/action features are synthesized in a speciﬁc form of h t , which serves as the latent representation for the past transitions at time t and is employed as input to predict forward dynamics f
( h t ) .
The error of the forward dynamics prediction is used to estimate the novelty r + t of the state at time t .
Furthermore, to make the latent features over the past transitions more informative, we also incorporate an inverse dynamics prediction model f inv to predict the action distributions.
Overall, the proposed dual-LSTM architecture enables us to perform sequence-level reasoning and inferring novelty from the multi-step forward prediction.
2. S EQUENCE E NCODING WITH D UAL -LSTM A RCHITECTURE
The sequence encoding module accepts a sequence of observations with length H and a sequence of actions with length L as input.
Formally, we denote the observation sequence and action sequence by O t =
o t − L − H − 1: t − L − 1 and A t = a t − L − 1: t − 1 , respectively.
Speciﬁcally, each observation o t is represented as a 3D image frame with width m , height n and channel c , i.e., o t ∈ R m × n × c .
Each action is modeled as a 1-hot encoding vector a t ∈ R | A | , where | A | denotes the size of the action space.
Given the sequences O t and A t , the sequence encoding module ﬁrst adopts an embedding module f e ( · ) parameterized by θ E = { θ E o , θ E a } to process the observation sequence and the action sequence as follows,
[Equation]
where θ E o and θ E a denote the parameters for the observation embedding function and the action embedding function, respectively.
Next, LSTM encoders are applied to the output of the observation/action embedding modules as follows,
[Equation]
where h ot ∈ R l and h at ∈ R l represent the latent features encoded from the observation sequence and action sequence.
For simplicity, we assume h ot and h at have the same dimensionality.
c ot and c at denote the cell output for the two LSTM modules.
Next, the sequence features for the observation/action h o t and h a t are synthesized to derive latent features h t which describe the past transitions.
Intuitively, the form of h t is proposed as follows:
[Equation]
To compute h t , an multiplicative interaction is ﬁrst performed over h ot and h at , which results in h itrt and (cid:12) denotes element-wise multiplication.
Then h t is derived by concatenating the multiplicative interaction feature h itrt with the latent representations for the observation and action sequences, i.e., h ot and h at .
The reason for generating h t in this way is that the prediction task over the partial observation o t is related to both the local information conveyed in the two sequences themselves (i.e., h ot and h at ), as well as the collaborative information derived via interacting the two sequence features in a form.
The reason for performing multiplicative interaction is that the advancement of such operation in synthesizing different types of features has been validated in prior works (Oh et al. , 2015; Ma et al. , 2019).
We demonstrate that generating h t in the proposed form is effective and crucial to derive a desirable policy learning performance in the ablation study (Figure 7c) of the experiment section.
2. C OMPUTING N OVELTY
To compute the novelty, the latent features h t are ﬁrst employed as input by a feedforward prediction function to predict the forward dynamics:
[Equation]
where f ( · ) is the forward prediction function parameterized by θ F , and ˆ ψ t denotes the prediction output.
We use ψ ∗ t to denote the prediction target, which is computed from some target function f ∗ ( · ) .
Within the proposed novelty framework, the target function f ∗ ( · ) could be derived in various forms, where the common choices include the representation of o t at its original feature space, i.g., image pixels, and the learned embedding of o t , i.e., f e ( · ; θ E o ) .
Apart from the conventional choices, in this work, we employ a target function computed from a random network distillation model (Burda et al. , 2019).
Thus, f ∗ ( · ) is represented by a ﬁxed and randomly initialized target network.
Intuitively, it forms a random mapping from each input observation to a point in a k -dimensional space, i.e., f ∗ : R m × n × c → R k .
Hence the forward dynamics model is trained to distill the randomly drawn function from the prior.
The prediction error inferred from such a model is related to the uncertainty quantiﬁcation in predicting some constant zero function (Osband et al. , 2018).
The novelty of a state is inferred from the uncertainty evaluated as the MSE loss for the forward model.
Formally, at step t , a novelty score or reward bonus is computed in the following form:
[Equation]
where β ≥ 0 is a hyperparameter to scale the reward bonus.
The reward bonus is issued to the agent in a step-wise manner.
During the policy learning process, the agent maximizes the sum over the external rewards and the intrinsic rewards derived from the novelty model.
Therefore, the overall reward term to be maximized as will be shown in (8) is computed as r t = r et + r + t , where r et denotes the external rewards from the environment.
2. L OSS F UNCTIONS FOR T RAINING
The training of the forward dynamics model is formulated as a regression problem.
The loss for optimizing the forward dynamics model is deﬁned as follows:
[Equation]
We additionally incorporate an inverse dynamics model f inv over the latent features h t to make them encode more abundant transition information.
Given the observation sequence O t with length H , the inverse model is trained to predict the H − 1 actions taken between the observations.
Thus, the inverse model is deﬁned as:
[Equation]
where f inv ( · ) denotes the inverse function parameterized by θ I , and p (ˆ a t − L − i ) denotes the action distribution output for time step t − L − i .
The inverse model is trained by minimizing a standard cross-entropy loss.
Overall, the forward loss and inverse loss are jointly optimized with the reinforcement learning objective.
Moreover, the parameters for the observation embedding module θ E o could be shared
[Figure]
with the policy model.
In summary, the compound objective function for deriving the intrinsically motivated reinforcement learning policy becomes:
[Equation]
(cid:34)(cid:88) t
[Equation]
, (8) where θ E , θ F and θ I are the parameters for the novelty model, θ π are the parameters for the policy model, L I ( · ) is the cross-entropy loss for the inverse model, 0 ≤ λ ≤ 1 is a weight to balance the loss for the forward and inverse models, and η ≥ 0 is the weight for maximizing the cumulative reward.
E XPERIMENTS 3. E XPERIMENTAL S ETUP
Task Domains For empirical evaluation, we adopt three 3D navigation tasks with ﬁrst-person view: 1) ‘ DoomMyWayHome-v0 ’ from ViZDoom (Kempka et al. , 2016); 2) ‘ Stairway to Melon ’ from DeepMind Lab
(Beattie et al. , 2016); 3) ‘ Explore Goal Locations ’ from DeepMind Lab.
The experiments in ‘ DoomMyWayHome-v0 ’ allow us to test the algorithms in scenarios with varying degrees of reward sparsity.
The experiments in ‘ Stairway to Melon ’ allow us to test the algorithms in scenarios with reward distractions.
The experiments in ‘ Explore Goal Locations ’ allow us to test the algorithms in scenarios with procedurally generated maze layout and random goal locations.
Baseline Methods For fare comparison, we adopt ‘LSTM-A3C’ as the RL algorithm for all the methods.
In the experiments, we compare with the vanilla ‘LSTM-A3C’ as well as the following intrinsic exploration baselines: 1) the Intrinsic Curiosity Module (Pathak et al. , 2017), denoted as ‘ICM’; 2) Episodic Curiosity through reachability (Savinov et al. , 2019), denoted as ‘EC’; 3) the
Random Network Distillation model, denoted as ‘RND’.
Our proposed Sequence-level Intrinsic exploration Module is denoted as ‘SIM’.
Our method adopt observation length 10 and action length 3 consistently for all domains.
All the intrinsic exploration baselines adopt non-sequential inputs.
The baseline ‘EC’ is a memory-based algorithm.
We shift the corresponding learning curves by the budgets of pretraining frames (i.e., 0.6M) in the results to be presented, following the original paper (Savinov et al. , 2019).
We present the implementation details for all the compared methods in
Appendix A.
3. E VALUATION WITH V ARYING R EWARD S PARSITY
Our ﬁrst empirical domain is a navigation task in the ‘ DoomMyWayHome-v0 ’ scenario from ViZDoom.
The task consists of a static maze layout and a ﬁxed goal location.
At the start of each episode, the agent spawns from one of the 17 spawning locations, as shown in Figure 3.
In this domain, we adopt three different setups with varying degree of reward sparsity, i.e., dense , sparse , and very sparse .
Under the dense setting, the agent spawns at one randomly selected location from the 17 locations and it is relatively easy to succeed in navigation.
Under the sparse and very sparse settings, the agent spawns at a ﬁxed location far away from the goal.
The environment issues a positive reward of +1 to the agent when reaching the goal.
Otherwise, the rewards are 0.
The episode terminates when the agent reaches the goal location or the episode length exceeds the time limit of 525 4-repeated steps.
We show the training curves measured in terms of navigation success ratio in Figure 4.
The results from Figure 4 depicts that as the rewards go sparser, the navigation would become more challenging.
The vanilla ‘LSTM-A3C’ algorithm could not progress at all under the sparse and very sparse settings.
‘ICM’ could not reach 100% success ratio under the sparse and very sparse settings, and so does ‘EC’ under the very sparse setting.
Our proposed method consistently achieves 100% success ratio across all the tasks with varying reward sparsity.
The detailed convergence scores are shown in Table 1.
We also present the results measured in terms of average episode length in Appendix B.3.
Our proposed solution also demonstrates signiﬁcant advantage in terms of convergence speed.
Though the reward sparsity varies, our method could quickly reach 100% success ratio in all the scenarios.
However, the convergence speeds of ‘ICM’, ‘EC’ and ‘RND’ apparently degrade with sparser rewards.
Also, we notice that the memory-based method (i.e., ‘EC’) takes much longer time to converge compared to the prediction-error based baselines ‘RND’ and ‘SIM’.
That is, the learning curves for those prediction-error based methods go up with a much steeper ratio compared to the memory-based method.
The reason might come from the memory that ‘EC’ keeps and updates at run-time to infer the novelty.
The novelty score assigned for each state might be unstable due to the run-time update to memory.
Moreover, ‘EC’ requires to pre-train the comparator module in some task domains such as ViZDoom, whereas our method, as well as ‘ICM’ and ‘RND’, does not require pre-training.
Overall, our proposed method could converge to 100% success ratio on average 3.3x as fast as ‘ICM’ and 2.1x compared to ‘RND’.
We present some detailed convergence statistics in
Appendix B.4.
3. E VALUATION WITH V ARYING M AZE L AYOUT AND G OAL L OCATION
Our second empirical evaluation engages a more dynamic navigation task with procedurally generated maze layout and randomly chosen goal locations.
We adopt the ‘Explore Goal Locations’ level script from DeepMind Lab.
At the start of each episode, the agent spawns at a random location and searches for a randomly deﬁned goal location within the time limit of 1350 4-repeated steps.
Each time the agent reaches the goal, it receives a reward of +10 and is spawned into another random location to search for the next random goal.
The maze layout is procedurally generated at the start of each episode.
This domain challenges the algorithms to derive general navigation behavior instead of relying on remembering the past trajectories.
We show the results with an environment interaction budget of 2M 4-repeated steps in Figure 5.
We exempt the baseline ‘EC’ in this task, because the pretraining of ‘EC’ consumes 0.6M interaction budgets, which makes it less feasible for the current task.
As a result, the method without intrinsic novelty model could only converge to an inferior performance around 10.
Our proposed method could score > 20 with less than 1M training steps, whereas ‘ICM’ and ‘RND’ take almost 2M steps [Figure]
[Table]
to score above 20 .
This demonstrates that our proposed algorithm could progress at a much faster speed compared to all the baselines under the procedurally generated maze setting.
3. E VALUATION WITH R EWARD D ISTRACTIONS
Our third empirical evaluation engages a cognitively complex task with reward distraction.
We adopt the ‘ Stairway to Melon ’ level script from DeepMind Lab.
In this task, the agent can follow either two corridors: one of them leads to a dead end, but has multiple apples along the way, collecting which the agent would receive a small positive reward of +1 ; the other corridor consists of one lemon which gives the agent a negative reward of − 1 , but after passing the lemon, there are stairs that lead to the navigation goal location upstairs indicated by a melon.
Collecting the melon makes the agent succeed in navigation and receive a reward of +20 .
The episode terminates when the agent reaches the goal location or the episode length exceeds the time limit of 525 4-repeated steps.
The results are shown in Figure 6.
We show both the cumulative episode reward and the success ratio for navigation.
Due to the reward distractions, the learning curves for each approach demonstrate instability with ubiquitous glitches.
The vanilla ‘LSTM-A3C’ could only converge to an inferior navigation success ratio of < 50% , and all the other baselines progress slowly.
Notably, our proposed method could fast grasp the navigation behavior under the reward distraction scenario, i.e., surpassing the standard of > 80% with less than 0 .
2 M environment interactions, which is at least 3x as fast as the compared baselines.
3. A BLATION S TUDY
In this section, we present the results for an ablation study under the very sparse task in ViZDoom.
Impact of multi-step prediction: We demonstrate that performing multi-step prediction could be beneﬁcial for policy training.
In Figure 4 (c), we have shown the comparison results with selfprediction baseline ‘RND’ and one-step prediction baseline ‘ICM’, both of which are feed-forward models.
In this section, we show the results by comparing with sequence-level one-step prediction baselines adapted from our proposed model.
From the results shown in Figure 7a, we notice that performing 3-step forward prediction would result in apparently better convergence than the ‘L1’ variants.
Expanding the scale of prediction difﬁculty by incorporating longer-term forward prediction would be beneﬁcial to derive high-quality novelty scores than one-step models.
[Figure]
Impact of inverse dynamics loss: We also investigate the impact of shaping the latent representation h t by incorporating the inverse dynamics loss.
To this end, we show the performance of our proposed model when the inverse dynamics is turned off in Figure 7b.
When performing short-term prediction, such as one-step look-ahead, the effect of inverse dynamics might not be very significant.
However, when considering longer term prediction, utilizing inverse dynamics loss could efﬁciently stabilize the training and help to shape the latent representation to be more meaningful (i.e., performance of H10-L3 (inv-off) is much worse than H10-L1 (inv-off)).
Impact of h t : We demonstrate that modeling h t in the proposed form of (3) is efﬁcient by comparing our method with the following two baseline models of h t : 1) only using the interactive features h itrt , denoted by ‘SIM-itr’, and 2) only using the concatenation of h ot and h at , denoted by ‘SIM-concat’.
From the results shown in Figure 7c, we ﬁnd that both baseline methods converge to inferior performance standard, i.e., the algorithm fail occasionally so that the averaged curve could not converge to 100% success ratio.
When using h t in the proposed form, the algorithm could consistently converge to 100% success ratio.
This demonstrates that modeling h t in our proposed form is crucial for deriving a desired policy learning performance.
Impact of the sequence/RND module: Lastly, we testify the efﬁciency of the two critical parts for our solution: 1) the sequence embedding module with dual-LSTM; 2) the RND module to compute the prediction target.
To this end, we create the following two baselines: 1) using a feedforward model together with RND, denoted by ‘SIM-no-Seq’, and 2) training the sequence embedding model with the target computed from the embedding function f e ( · ; θ E o ) instead of RND, denoted by ‘SIMno-RND’.
The results are shown in Figure 7d.
‘SIM-no-Seq’ could outperform the ‘ICM’ baseline, which indicates that using random network distillation to form the target could be more efﬁcient in representing the novelty of state than using the learned embedding function.
Also, ‘SIM-no-RND’ could converge much faster than ‘ICM’, which indicates that using the sequence-level modeling of novelty is more efﬁcient than using ﬂat concatenation of frames.
Overall, this study shows that using the sequence embedding model together with the RND prediction target is critical for deriving desirable performance.
R ELATED W ORK
Curiosity-driven exploration has been studied extensively in the reinforcement learning literature.
We refer the readers to (Oudeyer and Kaplan, 2009; Oudeyer et al. , 2007) for an overview.
In recent years, research on intrinsic exploration for deep reinforcement learning develops the novelty or curiosity model based on various factors, such as counts (Tang et al. , 2017; Choi et al. , 2019), pseudo-counts (Bellemare et al. , 2016; Ostrovski et al. , 2017), prediction-error (Achiam and Sastry, 2017; Stadie et al. , 2015) and information gain (Houthooft et al. , 2016; Nikolov et al. , 2019).
A prominent line of approaches for intrinsic exploration under partially observable settings fall under the prediction-error-based approaches.
Pathak et al.
(2017) propose a forward-backward dynamics model trained with self-supervision, and use the prediction loss of the forward model to infer the state novelty.
Oh and Cavallaro (2019) incorporate a triplet ranking function to push the prediction output of the forward model to be far from some alternative prediction output computed with wrong action inputs.
Apart from those prediction-error-based approaches, recently, Savinov et al.
(2019) propose a memory-based approach which forms a memory of novel states and trains a comparator network to model the reachability between states to assign state novelty.
While all the above mentioned approaches adopt visual inputs modeled as ﬂat concatenation of frames, we model the sequence-level novelty from past transition sequence.
Compared to the recent works that adopt sequence-level modeling in policy training (Chiappa et al. , 2017; Ke et al. , 2019), they mainly consider sequence-level policy, or construct dynamics models that are autoregressive.
In our work, we propose a dual-LSTM architecture that tackles open-loop multi-step dynamics prediction.
C ONCLUSION
In this paper, we tackle the challenge of improving policy training in sparse rewarded partially observable domains.
We propose a sequence-level novelty model, and we demonstrate the beneﬁt of such a model through various experimental domains, including tasks with partially observability as well as fully observable tasks.
In the future, we want to explore the possibility of adapting our proposed solution to derive modularized and transferable novelty model among related task domains.
A PPENDICES
This supplementary material is organized as follows.
First, we describe the implementation details for our proposed model and the baseline models.
Then we demonstrate the additional experiment results for the ViZDoom domains.
Besides, we show the task settings and hyperparameter settings to replicate the results shown for the ‘Stairway to Melon’ and ‘Explore Go Locations Small’ tasks in
DeepMind Lab.
Finally, we present the results on Atari experiments.
A I MPLEMENTATION D ETAILS A. SIM
The novelty model employs a sequence of observation frames with length H and a sequence of actions with length L as its input.
Speciﬁcally, each observation is modeled as RGB images of size 42 × 42 × 3 .
Each action is modeled as one-hot vector with size |A| , where A is the discrete action space used for each domain.
The observation embedding module f e ( · ; θ E o ) consists of two conv layers with 16 and 32 ﬁlters respectively.
Both layers use kernel size of 3 × 3 and stride of 2 .
The convolution layers are followed by a fc layer of size 256 .
The action embedding layer is a fc layer of size 128.
Then the state and action embedding outputs are fed to two LSTMs with latent size 256.
The synthesized latent feature h t has a size of 256 × 3 .
h t is fed to a fc layer of size 64 to construct the forward model (to predict RND target) and another fc layer of size ( H − 1) ∗ | A | followed by a softmax layer to construct the inverse model.
The inverse model predicts the previously taken actions with length H − 1 .
The target function f ∗ ( · ) is modeled by random network distillation function, for which we employ the same setting as introduced in Section A.3.
A. ICM
The ICM model takes an observation and an action as its input to predict the embedding computed for the observation of the next state.
The observation is modeled as 4 consequent gray-scale frames with size 42 × 42 × 4 .
The action input is modeled as an one-hot vector with size A .
We adopt the identical ICM implementation as the open-source code released for the original paper.
Speciﬁcally, the observation embedding model consists of 4 consequent conv layers, with ﬁlter size of 32 , kernel size of 3 × 3 and stride of 2 for each.
The output of the observation embedding is a vector of size 288.
The observation embedding is concatenated with the one-hot action to form a synthesized feature, which is fed to a fc layer of size 256 followed by another fc of size 288 to form the forward dynamics model.
A. RND
The RND mdoel takes an RGB image of size 42 × 42 × 3 as its input to predict the randomly projected target for that RGB image.
Speciﬁcally, the target function consists of 3 conv layers with 32 ﬁlters for each, kernel sizes of 8 , 4 and 3 , and strides of 4 , 2 and 1 , respectively.
The outputs of the last conv layer is followed by a fc layer of size 64 to compute the prediction target.
For all the layers, the weights are initialized by orthogonal initializer with scale of √ 2 and the biases for all the layers are initialized by 0 -initialization.
The prediction model consists of 4 consequent conv layers, with ﬁlter size of 32 , kernel size of 3 × 3 and stride of 2 for each.
The output of last conv layer is followed by a fc layer of size 64 to output the prediction.
A. EC
The comparitor network for ‘EC’ is implemented as Resnet-18 with 512 outputs.
The concatenated features for a pair of compared frames are fed to a fc layer of size 512, which is followed by a fc layer of size 2 and a softmax function to compute the classiﬁcation probability.
We adopt the identical implementation from the open-source code of the original paper.
A. LSTM-A3C
At each step, the ‘LSTM-A3C’ policy model takes an RGB image of size 42 × 42 × 3 as its input.
The image is ﬁrst processed by an embedding module, which consists of two conv layers withand 32 ﬁlters, kernel size of 3 × 3 , and stride of 2 for each.
Then the output of the last conv layer is fed to a fc layer of size 256 to form the input to the LSTM module.
We adopt single LSTM layer with a latent size of 256 .
The output of the LSTM module is fed to two brunches: one followed by a fc layer of size 1 to predict the value, another followed by a fc layer of size |A| and a softmax layer to predict the action probability.
To train the ’LSTM-A3C’, we use ADAM optimizer with learning rate of 1 e − 4 for all the task domains.
For ViZDoom tasks, we adopt 16 asynchronous actors and for DeepMind Lab tasks, we adopt 8 actors.
The value loss is weighted by 0 .
5 and the entropy regularization weight is 0.01.
B V I ZD OOM T ASKS B. T ASK S ETTINGS
We adopt the ‘DoomMyWayHome-v0’ scenario for the navigation tasks in ViZDoom.
Speciﬁcally, the tasks are static goal reaching tasks with a static maze layout.
The three task settings differ in terms of the agent’s spawn location.
Each episode lasts for 525 4-repeated simulator steps.
The episode terminates when the agent reaches the static goal location.
We adopt a discrete action space with size of 4: { move-left , move-right , forward , no-op } .
B. H YPERPARAMETER S ETTINGS
[Table]
[Table] [Table]
[Table] [Table]
ICM forward inverse ratio ( λ ) -
[Table] [Table]
RL loss coefﬁcient
[Table] [Table]
B. E VALUATION RESULT IN TERMS OF EPISODIC LENGTH
In this static goal reaching domain, the agent with better navigation policy would result in shorter path to reach the goal.
Therefore, we present the results evaluated in terms of average episodic length for each algorithm under the three task settings.
The results are shown in Figure 8.
We observe that the episodic lengths decrease at different ratios for the compared algorithms.
Notably, our algorithm decreases at a much faster ratio compared to all the baselines.
Meanwhile, the episodic length for both ‘SIM’ and ‘RND’ would converge to a better standard than the other methods.
B. E VALUATION RESULT IN TERMS OF C ONVERGENCE T IME
To qualitatively evaluate the advantage of our algorithm in terms of accelerating the policy learning convergence, we measure the average convergence time for each algorithm across the ViZDoom tasks.
The resuls are shown in Table 2.
For each algorithm, we present the approximated environment steps required for the algorithm to reach the convergence standard.
[Table]
B. A S TUDY ON THE I MPACT OF S CALING F ACTOR ( β )
In response to the reviewer’s comments, we provide a study on the impact of scaling factor on the tasks with both dense reward and sparse reward setting.
To this end, we present the result on the following two settings from ViZDoom: dense and verySparse .
Speciﬁcally, we testify the effect of policy training by investigating on the scaling factor from the following set: { 0 . 01 , 0 .
001 , 0 . 0001 } , where 0.001 is our recommended setting that works well across the ViZDoom domains and 0.01 and 0.0001 are the apparently large/small settings.
First, we present the policy training rewards under each scaling factor setting in Figure 9.
In the dense reward scenario, the policy could learn with both scaling factors of 0.001 and 0.0001.
However, when we set it to be 0.01, it would result in bias in behavior and lead to inferior task performance.
Thus, we could conclude that the dense reward tasks could still beneﬁt from such reward shaping with proper setting of the scaling factor.
For the verySparse setting, we observe that when the scaling factor is too small, its effect is very minimal and are not sufﬁce to let the policy learning progress.
Also, when it is set to be very large, it causes biased behavior and let the policy fail to learn proper behavior.
But generally, the suggested value 0.001 works well on all the cases.
[Figure]
We also present the scale of the intrinsic reward in Figure 10.
Overall, the intrinsic reward decreases as the training progresses, which means that our dynamics model is getting trained properly.
The result reveals that if we set the scaling factor to be too large, it would result in large intrinsic rewards and lead to inferior policy training performance.
[Figure]
B. A S TUDY ON THE I MPACT OF M ULTI - STEP S IZE ( L )
In response to the reviewer’s comments, we present a study on performing multi-step forward prediction with the size of forward prediction step (i.e., L ) selected from the following set { 1 , 2 , 3 , 4 , 5 } .
From the results shown in Figure 11 , we notice that performing multi-step prediction with our suggested L = 3 would have apparent advantage over L = 1 and L = 2 .
There is no apparent advantage for L = 4 and L = 5 over L = 3 .
Therefore, we suggest L = 3 as a recommended hyperparameter setting.
The phenomena that overlength prediction would not further beneﬁt policy learning could be explained as follows.
The open-loop forward prediction we introduce could efﬁciently scale up the prediction difﬁculty, i.e., the larget L , the more difﬁcult to predict.
When the prediction is too difﬁcult, the model leads to less favorable intrinsic reward bonus, among which the difference between prediction errors for novel states would be less distinguishable from those common states.
Therefore, performing multi-step forward prediction with moderate L would be ideal.
[Figure]
C ‘S TAIRWAY TO L EMON ’ T ASK C. T ASK S ETTINGS
We adopt the ‘Stairway to Lemon’ level script from DeepMind Lab to testify the algorithms under static goal reaching task with reward distraction.
This task engages a static maze and a static navigation target location.
Each episode terminates when the agent reaches the navigation location or the episodie length exceeds a predeﬁned time out of 2100 4-repeated simulator steps.
We adopt a discrete action space with size of 3: { move-left , move-right , forward } .
C. H YPERPARAMETER S ETTINGS
LSTM-A3C
ICM
RND EC SIM learning rate 1e1e- 1e1e- 1etask reward scale 0.
bonus reward scale0.
ICM forward inverse ratio ( λ ) - 0.
RL loss coefﬁcient ( η ) - 0.
C. E VALUATION IN TERMS OF EPISODIC LENGTH
In this task domain, we observe that the reward distractions would result in signiﬁcant instability to the learning process.
We show the evaluation result measured in terms of average episodic length in
Figure 12.
The result shows that our method leads to signiﬁcantly faster decrease in average episodic length compared to the baseline methods. [Figure] [Equation] [Figure]
[Equation] [Figure] [Equation] ASK S ETTINGS
We adopt the ‘Explore Goal Locations Small’ level script from DeepMind Lab to testify the algorithms under dynamic goal reaching settings.
Speciﬁcally, this task engages an episodically generated maze with a randomly speciﬁed goal location.
It challenges the learning algorithms to derive generalizable navigation behaviors that do not depend on remembering the static goal
[Table]
RL loss
[Table]
D. H YPERPARAMETER S ETTINGS E A TARI 2600 T ASKS E. H ARD E XPLORATION T ASKS
Though our exploration model is not designated for Atari tasks, we still get some results on the hard exploration Atari domains.
By investigating on the performance of our model in Atari tasks, we could evaluate the generality of our model on less partially observable domains.
At the same time, we could testify the scalability of our dynamics prediction model on tasks with relatively large action space.
In the experiment, we compare our method with the following two exploration baselines: ‘ICM’ and ‘RND’.
The algorithms are testiﬁed in the following two hard exloration Atari tasks: ms-pacman , which has 9 actions; solaris , which has 18 actions.
We implement the exploration models on top of the IMPALA framework.
Each compared method is run with identical environment settings.
The results are presented in Figure 13.
In ms-pacman , our proposed method could progress much faster than the two baselines.
Moreover, the model leads to much higher convergence performance than ‘ICM’ and ‘RND’.
In solaris , which is a challenging task in which each algorithm results in noisy learning curve with glitches, our method could achieve highest best score.
Overall, the results in Atari domains reveal that our novelty model is promising to work in a variety of task domains with different degree of observability.
E. D ENSE - REWARDED T ASK WITH L ARGE A CTION S PACE
In response to the reviewer’s comments, we provide experiment result on another complex dense reward task domain.
We take Seaquest from Atari 2600 as an example.
Besides dense reward, the task consists of another appealing characteristic which is that it has a relatively large action space that consists of 18 control actions.
Evaluating the method at this task domain could also help us to investigate whether our proposed forward dynamics-based reward shaping method could work on tasks with large action space.
The experiment result is shown in Figure 14.
The policy trained with our proposed method could progress signiﬁcantly faster than RND and ICM.
Moreover, our method also leads to better convergence reward compared to the baselines.
It demonstrates that our proposed method could beneﬁt the dense-rewarded tasks as well.
Moreover, it also shows the generality of our proposed solution to tackle a broad range of RL tasks, not being restricted to deal with only partially observable navigation tasks.