Near-optimal Policy Optimization Algorithms for Learning Adversarial Linear Mixture MDPs
This provides a near-optimal solution for reinforcement learning in adversarial environments with linear structure, which is incremental but improves regret bounds.
The paper tackles the problem of learning Markov decision processes with adversarial rewards and linear mixture transitions, proposing the POWERS algorithm that achieves $ ilde{O}(dH\sqrt{T})$ regret and proves a matching lower bound.
Learning Markov decision processes (MDPs) in the presence of the adversary is a challenging problem in reinforcement learning (RL). In this paper, we study RL in episodic MDPs with adversarial reward and full information feedback, where the unknown transition probability function is a linear function of a given feature mapping, and the reward function can change arbitrarily episode by episode. We propose an optimistic policy optimization algorithm POWERS and show that it can achieve $\tilde{O}(dH\sqrt{T})$ regret, where $H$ is the length of the episode, $T$ is the number of interactions with the MDP, and $d$ is the dimension of the feature mapping. Furthermore, we also prove a matching lower bound of $\tildeΩ(dH\sqrt{T})$ up to logarithmic factors. Our key technical contributions are two-fold: (1) a new value function estimator based on importance weighting; and (2) a tighter confidence set for the transition kernel. They together lead to the nearly minimax optimal regret.