NeurIPS 2020

### Review 1

Summary and Contributions: This paper introduces a method for efficient exploration in RL. The proposed method assumes an MDP with high-dimensional states that are generated by an underlying lower-dimensional process, such that these states can be compressed via an unsupervised learning algorithm/oracle. The method then (1) defines an MDP over the resulting low-dimensional state space; and (2) learns a policy by generating trajectories in low-dimensional space, which arguably facilitates exploration. At each iteration, the algorithm gathers data to compute a policy and also to improve the embedding model computed by the unsupervised algorithm. The authors show that as long as the unsupervised algorithm and the tabular RL algorithm have polynomial sample complexity, it is possible to find a near-optimal policy with polynomial complexity in the number of latent states, which is much smaller than the number of high-dimensional states. The authors show experiments on simple synthetic domains, where their framework presents good performance.

Strengths: This is a well-written (mostly theoretical) paper. Although it demonstrates empirically that the proposed method works in simple problems, the underlying theory seems sound and the formal results that are presented are not trivial.

Weaknesses: The theory underlying this method seems well-developed. I am curious, however, about whether it would perform well in more realistic problems. Your experiments are done in synthetic domains with highly structured high-dimensional states that, by construction, have a clear and well-defined low-dimensional representation. Most realistic problems where high-dimensional states are a problem, however, require the use of (non-linear) value function approximation, which (I believe) is not allowed in your framework. Do you believe that your method could nonetheless be applied to more realistic settings? Furthermore, it is not clear to me that the proposed method actually improves learning by (as the title suggests) exploring more efficiently. Is it fair/accurate to say that you are efficiently exploring? It seems like your method is not really guiding exploration, but it is instead solving a low-dimensional version of the original problem. Although this may accelerate learning, faster learning results from having of a smaller MDP, not from using a method that explicitly explores efficiently. In fact, the tabular algorithm could explore using a random policy and it would still have the desired properties required by your framework.

Correctness: The theory underlying the results seems correct. The empirical methodology seems correct.

Clarity: The paper is generally well-written.

Relation to Prior Work: Related work is properly discussed.

Reproducibility: Yes

Additional Feedback: This paper introduces a method for efficient exploration in RL. The proposed method assumes an MDP with high-dimensional states that are generated by an underlying lower-dimensional process, such that these states can be compressed via an unsupervised learning algorithm/oracle. The method then (1) defines an MDP over the resulting low-dimensional state space; and (2) learns a policy by generating trajectories in low-dimensional space, which arguably facilitates exploration. At each iteration, the algorithm gathers data to compute a policy and also to improve the embedding model computed by the unsupervised algorithm. The authors show that as long as the unsupervised algorithm and the tabular RL algorithm have polynomial sample complexity, it is possible to find a near-optimal policy with polynomial complexity in the number of latent states, which is much smaller than the number of high-dimensional states. The authors show experiments on simple synthetic domains, where their framework presents good performance. I have a few questions and comments: 1) What is the technical reason why the reward function needs to depend on the time step within an episode? 2) In most RL problems, the exact horizon H is unknown. Does your method support learning in those settings? 3) Are "levels" the same as time steps within the episode? 4) Related to the question above: my understanding is that you need to compute one embedding/unsupervised model per time step/level in the episode. If this is the case, why is this required? 5) On line 216, you say that the learning process needs to be executed for N times to ensure that the algorithm succeeds with high probability. Why do you need to run the algorithm several times, to avoid a failure, given that it should (in theory, if all of its components have polynomial sample complexity) always converge to a near-optimal solution? 6) Most unsupervised learning algorithms for computing embeddings return continuous low-dimensional representations of the input data. How do you address this issue, given that (if I understand this correctly) the policy for the underlying MDP M' needs to be identified by a tabular RL algorithm, which operates over discrete/finite state representations? 7) Is it fair/accurate to say that you are efficiently exploring? It seems like your method is not really guiding exploration, but it is instead solving a low-dimensional version of the original problem. Although this may accelerate learning, faster learning results from having of a smaller MDP, not from using a method that explicitly explores efficiently. In fact, the tabular algorithm could explore using a random policy and it would still have the desired properties required by your framework. 8) Your experiments are done in synthetic domains with highly structured high-dimensional states that, by construction, have a clear and well-defined low-dimensional representation. Most realistic problems where high-dimensional states are a problem, however, require the use of (non-linear) value function approximation, which (I believe) is not allowed in your framework. Do you believe that your method could nonetheless be applied to more realistic settings? ************************ POST-REBUTTAL COMMENTS I have read the authors' rebuttal and thank them for addressing my questions and suggestions. I believe that they have satisfactorily addressed the main points that I brought up, and I therefore keep my original overall positive view on this submission.

### Review 2

Summary and Contributions: The paper studies exploration in reinforcement learning using unsupervised learning oracles. They derive a polynomial algorithm for Block Markov Decision Process when the unsupervised learning method has polynomial complexity. The method appears to be both theoretically as well as empirically strong. ======= Unchanged after rebuttal

Strengths: - the paper opens a new interesting research direction using unsupervised learning methods; this has not been studied before on the theoretical side for reinforcement learning exploration. - Removing the minimum visitation probably requirement of the prior work of Du et al '19 on block MDPs is another big contribution by itself.

Weaknesses: - no major limitations; this is a first step in a certain direction of research. The bound is vaguely stated as polynomial'' which means there is a lot of room for further studies in the area.

Correctness: Yes

Clarity: Yes

Relation to Prior Work: Yes

Reproducibility: Yes

### Review 3

Summary and Contributions: This work examines the utility of unsupervised learning for efficient exploration on reinforcement learning tasks. The proposed framework is based on two main components: an unsupervised learning algorithm and a no-regret tabular reinforcement learning algorithm. Roughly speaking, the unsupervised learning oracle encodes the state space in such a way that similar states are clustered together. Then, we are able to apply any no-regret tabular reinforcement learning algorithm on the new state space (it is referred as latent space in the paper). Authors prove that the proposed framework is able to find a near-optimal policy with sample complexity polynomial in the number of latent states, which is significantly smaller than the number of possible observations. Experiments have been conducted on two hard for exploration environments, the LockBernoulli and the LockGaussian, where different unsupervised learning algorithms and tabular RL algorithms have been examined.

Strengths: Authors propose a new algorithmic framework for the Block Markov Decision Process that is based on an unsupervised learning oracle and a tabular RL algorithm to find a near-optimal policy. The main contribution of this work is its theoretical analysis that proves the efficiency of the proposed algorithmic scheme. More specifically, it has been proved that the proposed framework is able to find a near-optimal policy with sample complexity polynomial in the number of latent states, which is significantly smaller than the number of possible observations. Moreover, the impact of the unsupervised algorithm on the performance of the proposed framework has been examined.

Weaknesses: The proposed framework assumes that we have access to an unsupervised learning oracle (ULO) and an (ε, δ)-correct episodic no-regret algorithm. In general this assumption is a little bit restricted as the performance of the proposed framework is highly depending on the ability of the unsupervised learning scheme to discover the latent space. Nevertheless, the theoretical analysis of the framework doesn't consider the probability the unsupervised learning oracle to encode inappropriately the observations. Also the training of the ULO is not explained in details. I think that the ULO is the key component of the proposed framework and it can have a huge impact on its performance. Moreover, authors should examine and/or to discuss its applicability of the proposed framework on more challenging environments.

Correctness: In my opinion the framework introduced in this work along with the presented empirical methodology are correct.

Clarity: In general the paper is well written and the reader can easily understand the main idea of the paper. The only part of the paper that need to be revised is the description of the label matching process. I found this part a little bit confused and some parts of Alg.2 should be explained in a more clear way. For instance, what is the purpose of the training data?

Relation to Prior Work: The related work is presented clearly in the paper and the author discuss in details the motivation and how this work differs from previous contributions.

Reproducibility: Yes

Additional Feedback: See my comments on the previous sections. I would like to thank authors for their rebuttal. Having also read other reviews, I decided to keep my original positive evaluation.

### Review 4

Summary and Contributions: This paper proposes an algorithmic framework that can combine unsupervised learning oriacle with tabular RL method. There is theoretical guarantee that when both parts are in polynomial sample complexity, the near optimal policy can be found. The instantiation of this method ourperforms previous methods.

Strengths: This is the first provable method that can be applied in relatively large observation space. The unified framework is general can in theory can be used with any unsupervised learning methods and tabular RL algo.

Weaknesses: Some curves in the experiments are lack of error bar and clarification in the caption --- is this 1 standard deviation? More qualitative visualized demonstrations of the task would be helpful for understanding the environment.

Correctness: The proposed theory is correct from my perspective. And the experiments along with the theory confirm the claim of the authors. I believe the results are sound and valid.

Clarity: The paper is well written. The paper is written in formal and fluent language. There are small typos, however.

Relation to Prior Work: The discussion is clear and sufficient. The discussion includes previous works especially those that inspire this work. They further differentiate their method with previous method. I believe there are more that can be added such as the difference between their setting and real-world settings used in empirical papers. This can be really useful for practitioners to create new algorithms.

Reproducibility: Yes