Optimistic MLE -- A Generic Model-based Algorithm for Partially Observable Sequential Decision Making

TL;DR

This paper presents OMLE, a unified, efficient model-based algorithm that learns near-optimal policies in a broad class of partially observable sequential decision-making problems, including new challenging settings.

Contribution

Introduces OMLE, a generic algorithm combining optimism and maximum likelihood estimation, capable of handling diverse POMDPs and partially observable RL problems with polynomial sample complexity.

Findings

Learns near-optimal policies in various POMDPs and RL problems.

First sample complexity for observable POMDPs with continuous observations.

Effective in low-rank and SAIL condition problems.

Abstract

This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable POMDPs and multi-step decodable POMDPs), but also many new challenging RL problems especially in the partially observable setting that were not previously known to be tractable. Notably, the new problems addressed by this paper include (1) observable POMDPs with continuous observation and function approximation, where we achieve the first sample complexity that is completely independent of the size of observation space; (2) well-conditioned low-rank sequential decision making problems (also known as Predictive State Representations (PSRs)), which include and generalize all known tractable POMDP examples under a more intrinsic representation; (3) general sequential decision making problems under SAIL condition, which unifies our existing understandings of model-based RL in both fully observable and partially observable settings. SAIL condition is identified by this paper, which can be viewed as a natural generalization of Bellman/witness rank to address partial observability. This paper also presents a reward-free variant of OMLE algorithm, which learns approximate dynamic models that enable the computation of near-optimal policies for all reward functions simultaneously.