Robust Average-Reward Markov Decision Processes

• URL: http://arxiv.org/abs/2301.00858v1
• Date: Mon, 2 Jan 2023 19:51:55 GMT
• Title: Robust Average-Reward Markov Decision Processes
• Authors: Yue Wang, Alvaro Velasquez, George Atia, Ashley Prater-Bennette, Shaofeng Zou
• Abstract summary: We focus on robust average-reward MDPs, where the goal is to find a policy that optimize the worst-case average reward over an uncertainty set. We take an approach that approximates average-reward MDPs using discounted MDPs. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value algorithm that provably finds its solution.
• Score: 25.125481838479256
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

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