Distributionally Robust Optimization for Sequential Decision Making

TL;DR

This paper develops a tractable framework for distributionally robust Markov Decision Processes that integrates generalized moment and statistical distance information, enabling robust sequential decision making under uncertainty.

Contribution

It introduces a unified ambiguity set format that combines moment and statistical distance information, extending prior models and maintaining tractability.

Findings

The proposed approach remains computationally tractable under mild conditions.

Distributionally robust policies can be obtained via a sequence of convex optimization problems.

The framework effectively incorporates empirical data and uncertainty information.

Abstract

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we study distributionally robust MDPs where ambiguity sets for the uncertain parameters are of a format that can easily incorporate in its description the uncertainty's generalized moment as well as statistical distance information. In this way, we generalize existing works on distributionally robust MDP with generalized-moment-based and statistical-distance-based ambiguity sets to incorporate information from the former class such as moments and dispersions to the latter class that critically depends on empirical observations of the uncertain parameters. We show that, under this format of ambiguity sets, the resulting distributionally robust MDP remains tractable under mild technical conditions. To be more specific, a distributionally robust policy can be constructed by solving a sequence of one-stage convex optimization subproblems.