Solving Long-run Average Reward Robust MDPs via Stochastic Games

TL;DR

This paper introduces a new approach to solving long-run average reward robust MDPs with polytopic uncertainty sets by reducing the problem to stochastic games, leading to novel complexity bounds and an efficient policy iteration algorithm.

Contribution

It presents a reduction of polytopic RMDPs to stochastic games, establishes new complexity bounds, and proposes Robust Polytopic Policy Iteration (RPPI) for improved efficiency.

Findings

Threshold decision problem is in NP ∩ coNP.

RPPI outperforms existing value iteration methods.

New complexity bounds for polytopic RMDPs.

Abstract

Markov decision processes (MDPs) provide a standard framework for sequential decision making under uncertainty. However, MDPs do not take uncertainty in transition probabilities into account. Robust Markov decision processes (RMDPs) address this shortcoming of MDPs by assigning to each transition an uncertainty set rather than a single probability value. In this work, we consider polytopic RMDPs in which all uncertainty sets are polytopes and study the problem of solving long-run average reward polytopic RMDPs. We present a novel perspective on this problem and show that it can be reduced to solving long-run average reward turn-based stochastic games with finite state and action spaces. This reduction allows us to derive several important consequences that were hitherto not known to hold for polytopic RMDPs. First, we derive new computational complexity bounds for solving long-run average reward polytopic RMDPs, showing for the first time that the threshold decision problem for them is in $NP \cap coNP$ and that they admit a randomized algorithm with sub-exponential expected runtime. Second, we present Robust Polytopic Policy Iteration (RPPI), a novel policy iteration algorithm for solving long-run average reward polytopic RMDPs. Our experimental evaluation shows that RPPI is much more efficient in solving long-run average reward polytopic RMDPs compared to state-of-the-art methods based on value iteration.