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Robust reinforcement learning (RL) aims to find a policy that optimizes theworst-case performance in the face of uncertainties. In this paper, we focus onaction robust RL with the probabilistic policy execution uncertainty, in which,instead of always carrying out the action specified by the policy, the agentwill take the action specified by the policy with probability $1-\rho$ and analternative adversarial action with probability $\rho$. We establish theexistence of an optimal policy on the action robust MDPs with probabilisticpolicy execution uncertainty and provide the action robust Bellman optimalityequation for its solution. Furthermore, we develop Action Robust ReinforcementLearning with Certificates (ARRLC) algorithm that achieves minimax optimalregret and sample complexity. Furthermore, we conduct numerical experiments tovalidate our approach's robustness, demonstrating that ARRLC outperformsnon-robust RL algorithms and converges faster than the robust TD algorithm inthe presence of action perturbations.

Efficient Action Robust Reinforcement Learning with Probabilistic Policy Execution Uncertainty