Solving Non-Rectangular Reward-Robust MDPs via Frequency Regularization
This work addresses performance sensitivity issues in RMDPs for reinforcement learning practitioners, but it is incremental as it focuses on a specific non-rectangular case with fixed transitions.
The paper tackled the problem of overly conservative behavior in robust Markov decision processes (RMDPs) due to the rectangularity condition, by studying non-rectangular reward-RMDPs and connecting them to policy visitation frequency regularization, resulting in a policy-gradient method that demonstrated less conservative behavior in numerical experiments.
In robust Markov decision processes (RMDPs), it is assumed that the reward and the transition dynamics lie in a given uncertainty set. By targeting maximal return under the most adversarial model from that set, RMDPs address performance sensitivity to misspecified environments. Yet, to preserve computational tractability, the uncertainty set is traditionally independently structured for each state. This so-called rectangularity condition is solely motivated by computational concerns. As a result, it lacks a practical incentive and may lead to overly conservative behavior. In this work, we study coupled reward RMDPs where the transition kernel is fixed, but the reward function lies within an $α$-radius from a nominal one. We draw a direct connection between this type of non-rectangular reward-RMDPs and applying policy visitation frequency regularization. We introduce a policy-gradient method and prove its convergence. Numerical experiments illustrate the learned policy's robustness and its less conservative behavior when compared to rectangular uncertainty.