Nearly Optimal Latent State Decoding in Block MDPs
This work addresses the challenge of efficiently learning optimal policies in environments with rich observations but few latent states, which is incremental as it builds on existing Block MDP frameworks.
The paper tackles the problem of model estimation and reward-free learning in episodic Block MDPs, deriving an information-theoretical lower bound for estimating the latent state decoding function and presenting an algorithm that approaches this limit, with sample complexity improvements by a multiplicative factor n under certain conditions.
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.