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Robust Markov Decision Processes (MDPs) offer a promising framework for computing reliable policies under model uncertainty. While policy gradient methods have gained increasing popularity in robust discounted MDPs, their application to the average-reward criterion remains largely unexplored. This paper proposes a Robust Projected Policy Gradient (RP2G), the first generic policy gradient method for robust average-reward MDPs (RAMDPs) that is applicable beyond the typical rectangularity assumption on transition ambiguity. In contrast to existing robust policy gradient algorithms, RP2G incorporates an adaptive decreasing tolerance mechanism for efficient policy updates at each iteration. We also present a comprehensive convergence analysis of RP2G for solving ergodic tabular RAMDPs. Furthermore, we establish the first study of the inner worst-case transition evaluation problem in RAMDPs, proposing two gradient-based algorithms tailored for rectangular and general ambiguity sets, each with provable convergence guarantees. Numerical experiments confirm the global convergence of our new algorithm and demonstrate its superior performance. 

Optimizing risk-averse objectives in discounted MDPs is challenging because most models do not admit direct dynamic programming equations and require complex history-dependent policies. In this paper, we show that the risk-averse total reward criterion, under the Entropic Risk Measure (ERM) and Entropic Value at Risk (EVaR) risk measures, can be optimized by a stationary policy, making it simple to analyze, interpret, and deploy. We propose exponential value iteration, policy iteration, and linear programming to compute optimal policies. Compared with prior work, our results only require the relatively mild condition of transient MDPs and allow for both positive and negative rewards. Our results indicate that the total reward criterion may be preferable to the discounted criterion in a broad range of risk-averse reinforcement learning domains. 

We study the problem of imitation learning via inverse reinforcement learning where the agent attempts to learn an expert's policy from a dataset of collected state, action tuples. We derive a new Robust model-based Offline Imitation Learning method (ROIL) that mitigates covariate shift by avoiding estimating the expert's occupancy frequency. Frequently in offline settings, there is insufficient data to reliably estimate the expert's occupancy frequency and this leads to models that do not generalize well. Our proposed approach, ROIL, is a method that is guaranteed to recover the expert's occupancy frequency and is efficiently solvable as an LP. We demonstrate ROIL's ability to achieve minimal regret in large environments under covariate shift, such as when the state visitation frequency of the demonstrations does not come from the expert.