Adversarially Trained Actor Critic for offline CMDPs

We propose a Safe Adversarial Trained Actor Critic (SATAC) algorithm for offline reinforcement learning (RL) with general function approximation in the presence of limited data coverage. SATAC operates as a two-player Stackelberg game featuring a refined objective function. The actor (leader player) optimizes the policy against two adversarially trained value critics (follower players), who focus on scenarios where the actor's performance is inferior to the behavior policy. Our framework provides both theoretical guarantees and a robust deep-RL implementation. Theoretically, we demonstrate that when the actor employs a no-regret optimization oracle, SATAC achieves two guarantees: (i) For the first time in the offline RL setting, we establish that SATAC can produce a policy that outperforms the behavior policy while maintaining the same level of safety, which is critical to designing an algorithm for offline RL. (ii) We demonstrate that the algorithm guarantees policy improvement across a broad range of hyperparameters, indicating its practical robustness. Additionally, we offer a practical version of SATAC and compare it with existing state-of-the-art offline safe-RL algorithms in continuous control environments. SATAC outperforms all baselines across a range of tasks, thus validating the theoretical performance.