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Policy Optimization (PO) is one of the most popular methods in ReinforcementLearning (RL). Thus, theoretical guarantees for PO algorithms have becomeespecially important to the RL community. In this paper, we study PO inadversarial MDPs with a challenge that arises in almost every real-worldapplication -- \textit{delayed bandit feedback}. We give the first near-optimalregret bounds for PO in tabular MDPs, and may even surpass state-of-the-art(which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easyto implement and to generalize, allowing us to extend our algorithm to: (i)infinite state space under the assumption of linear $Q$-function, proving thefirst regret bounds for delayed feedback with function approximation. (ii) deepRL, demonstrating its effectiveness in experiments on MuJoCo domains.

Delay-Adapted Policy Optimization and Improved Regret for Adversarial MDP with Delayed Bandit Feedback