Nearly Optimal Latent State Decoding in Block MDPs

TL;DR

This paper develops near-optimal algorithms for decoding latent states and learning policies in block MDPs, achieving fundamental limits and improving sample complexity under certain conditions.

Contribution

It introduces an algorithm that approaches the information-theoretical lower bound for latent state decoding and demonstrates near-optimal policy learning in reward-free settings.

Findings

Derived an information-theoretical lower bound for decoding error.

Presented an algorithm approaching this fundamental limit.

Showed that exploiting block structure can significantly reduce sample complexity.

Abstract

We investigate the problems of model estimation and reward-free learning in episodic Block MDPs. In these MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are first interested in estimating the latent state decoding function (the mapping from the observations to latent states) based on data generated under a fixed behavior policy. We derive an information-theoretical lower bound on the error rate for estimating this function and present an algorithm approaching this fundamental limit. In turn, our algorithm also provides estimates of all the components of the MDP. We then study the problem of learning near-optimal policies in the reward-free framework. Based on our efficient model estimation algorithm, we show that we can infer a policy converging (as the number of collected samples grows large) to the optimal policy at the best possible rate. Interestingly, our analysis provides necessary and sufficient conditions under which exploiting the block structure yields improvements in the sample complexity for identifying near-optimal policies. When these conditions are met, the sample complexity in the minimax reward-free setting is improved by a multiplicative factor $n$, where $n$ is the number of possible contexts.