Online MDP with Transition Prototypes: A Robust Adaptive Approach

TL;DR

This paper introduces an online robust MDP algorithm that leverages transition prototypes and adaptive ambiguity sets to efficiently identify true transition kernels, ensuring robust policies with sublinear regret and improved early-stage performance.

Contribution

It proposes a novel online robust MDP method using transition prototypes and adaptive ambiguity sets, with theoretical guarantees and practical improvements over existing approaches.

Findings

Achieves sublinear regret in identifying optimal robust policies.

Provides an early stopping mechanism with worst-case value function bounds.

Outperforms existing methods in numerical experiments, especially with limited data.

Abstract

In this work, we consider an online robust Markov Decision Process (MDP) where we have the information of finitely many prototypes of the underlying transition kernel. We consider an adaptively updated ambiguity set of the prototypes and propose an algorithm that efficiently identifies the true underlying transition kernel while guaranteeing the performance of the corresponding robust policy. To be more specific, we provide a sublinear regret of the subsequent optimal robust policy. We also provide an early stopping mechanism and a worst-case performance bound of the value function. In numerical experiments, we demonstrate that our method outperforms existing approaches, particularly in the early stage with limited data. This work contributes to robust MDPs by considering possible prior information about the underlying transition probability and online learning, offering both theoretical insights and practical algorithms for improved decision-making under uncertainty.