Model-Free Robust Average-Reward Reinforcement Learning
This work addresses robust decision-making in uncertain environments for reinforcement learning practitioners, but it is incremental as it extends existing robust MDP methods to the average-reward setting.
The paper tackles robust average-reward reinforcement learning under model uncertainty by designing two model-free algorithms, robust RVI TD and robust RVI Q-learning, and proves their convergence to optimal solutions with theoretical analysis of the robust Bellman equation.
Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence and Wasserstein distance.