Near-Optimal Learning and Planning in Separated Latent MDPs

TL;DR

This paper investigates the learning and planning challenges in Latent Markov Decision Processes, establishing near-optimal statistical thresholds and computational algorithms under separation assumptions.

Contribution

It introduces a nearly-sharp statistical threshold for horizon length in LMDPs and presents a quasi-polynomial algorithm with matching lower bounds under separation assumptions.

Findings

Established a statistical threshold for efficient learning in LMDPs.

Developed a quasi-polynomial time algorithm under separability assumptions.

Proved near-matching lower bounds under the exponential time hypothesis.

Abstract

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known impossibility results, we consider several notions of separation of the constituent MDPs. The main thrust of this paper is in establishing a nearly-sharp *statistical threshold* for the horizon length necessary for efficient learning. On the computational side, we show that under a weaker assumption of separability under the optimal policy, there is a quasi-polynomial algorithm with time complexity scaling in terms of the statistical threshold. We further show a near-matching time complexity lower bound under the exponential time hypothesis.