Provably Efficient Exploration in Policy Optimization

While policy-based reinforcement learning (RL) achieves tremendous successes in practice, it is significantly less understood in theory, especially compared with value-based RL. In particular, it remains elusive how to design a provably efficient policy optimization algorithm that incorporates exploration. To bridge such a gap, this paper proposes an \underline{O}ptimistic variant of the \underline{P}roximal \underline{P}olicy \underline{O}ptimization algorithm (OPPO), which follows an "optimistic version" of the policy gradient direction. This paper proves that, in the problem of episodic Markov decision process with unknown transition and full-information feedback of adversarial reward, OPPO achieves an $\tilde{O}(\sqrt{|\mathcal{S}|^2|\mathcal{A}|H^3 T})$ regret. Here, $|\mathcal{S}|$ is the size of the state space, $|\mathcal{A}|$ is the size of the action space, $H$ is the episode horizon, and $T$ is the total number of steps. To the best of our knowledge, OPPO is the first provably efficient~policy optimization algorithm that explores.