Rate-Optimal Policy Optimization for Linear Markov Decision Processes

TL;DR

This paper introduces a policy optimization method that achieves the best possible regret bounds in linear Markov Decision Processes, both in stochastic and adversarial settings, advancing the theoretical understanding of optimal learning rates.

Contribution

It is the first to establish rate-optimal regret bounds for policy optimization in linear MDPs in both stochastic and adversarial feedback scenarios.

Findings

Achieves $ ilde{O}( oot K)$ regret in stochastic setting.

Establishes optimal regret bounds in adversarial setting.

First to provide rate guarantees for policy optimization in these contexts.

Abstract

We study regret minimization in online episodic linear Markov Decision Processes, and obtain rate-optimal $\widetilde O (\sqrt K)$ regret where $K$ denotes the number of episodes. Our work is the first to establish the optimal (w.r.t.~$K$) rate of convergence in the stochastic setting with bandit feedback using a policy optimization based approach, and the first to establish the optimal (w.r.t.~$K$) rate in the adversarial setup with full information feedback, for which no algorithm with an optimal rate guarantee is currently known.