Provably efficient RL with Rich Observations via Latent State Decoding (1901.09018v3)

Abstract: We study the exploration problem in episodic MDPs with rich observations generated from a small number of latent states. Under certain identifiability assumptions, we demonstrate how to estimate a mapping from the observations to latent states inductively through a sequence of regression and clustering steps -- where previously decoded latent states provide labels for later regression problems -- and use it to construct good exploration policies. We provide finite-sample guarantees on the quality of the learned state decoding function and exploration policies, and complement our theory with an empirical evaluation on a class of hard exploration problems. Our method exponentially improves over $Q$-learning with na\"ive exploration, even when $Q$-learning has cheating access to latent states.

• The paper introduces a novel latent state decoding algorithm that reduces rich-observation environments to tabular Markov Decision Processes, ensuring efficient exploration.
• It guarantees finite-sample performance improvements over traditional Q-learning by developing effective exploration policies using an ε-policy cover.
• This approach is applicable to high-dimensional domains like robotics, bridging theoretical advancements and practical reinforcement learning challenges.

Provably Efficient Reinforcement Learning with Rich Observations via Latent State Decoding

The paper "Provably Efficient RL with Rich Observations via Latent State Decoding" presents a novel method for addressing the exploration challenge in reinforcement learning (RL) environments characterized by rich observations, such as images and texts. These environments, modeled as episodic Markov Decision Processes (MDPs) with a small number of latent states, pose unique challenges due to the large and complex observation spaces that cannot be handled efficiently by traditional tabular methods. The fundamental contribution of this work is an algorithmic approach that combines structural assumptions about latent states with function approximation and empirical risk minimization to construct exploration policies that can efficiently handle these complex environments.

Key Contributions

1. Latent State Decoding Function: The authors introduce a method to inductively estimate a mapping from observed data to latent states using a sequence of regression and clustering steps. This approach allows them to reduce the problem with rich observations to a tabular MDP, making exploration in complex spaces tractable.
2. Sample Efficiency Guarantees: The proposed algorithm provides finite-sample guarantees on the quality of learned state decoding functions and exploration policies. In particular, their method shows exponential improvement over Q-learning with na\"ive exploration, even in settings where Q-learning has access to latent states.
3. Block Markov Decision Processes (BMDPs): The paper formalizes a new class of MDPs called BMDPs, which accommodate rich observation spaces by assuming a block-structured emission process, thus partitioning the observation space into blocks corresponding to latent states.
4. Policy Cover Exploration: The authors define and utilize the concept of an $\epsilon$-policy cover, which is a set of policies that can explore each state with maximum reaching probability up to $\epsilon$. This innovation is crucial for constructing effective exploration policies in settings where state space is directly unobservable but has latent structure.

Numerical Results and Implications

The empirical evaluation demonstrates the efficacy of the proposed approach in a variety of challenging environments characterized by difficult exploration problems. The method exhibits significant improvements over traditional Q-learning and performs close to the optimal, even when Q-learning operates with privileged information about latent states. These strong numerical results highlight the practical potential of the algorithm.

Implications and Future Work

The practical implications of this research are significant, especially for applications that involve rich sensory inputs, such as robotics and autonomous systems, where observations are fundamentally high-dimensional. Theoretically, this work contributes to understanding sample-efficient exploration in RL by incorporating latent-state modeling.

Future work could extend these techniques to settings with weaker assumptions about the observations or relaxing the block-structure requirement. Moreover, addressing computational intractability in certain high-dimensional function classes or dealing with non-Markovian structures would advance the applicability of this approach further.

Conclusion

The paper provides a robust framework for efficiently exploring in reinforcement learning settings characterized by rich observations, leveraging latent state structure. By extending and enriching our algorithmic toolkit with latent state decoding, this work bridges a critical gap between theoretical RL research and practical applications in domains with high-dimensional input.