Rate-Optimal Policy Optimization for Linear Markov Decision Processes
This provides optimal regret guarantees for reinforcement learning in linear MDPs, addressing a theoretical gap in both stochastic and adversarial settings.
The paper tackles regret minimization in online episodic linear Markov Decision Processes, achieving rate-optimal $\widetilde O (\sqrt K)$ regret where $K$ is the number of episodes. It establishes the first optimal rate in stochastic settings with bandit feedback using policy optimization and the first optimal rate in adversarial setups with full information feedback.
We study regret minimization in online episodic linear Markov Decision Processes, and obtain rate-optimal $\widetilde O (\sqrt K)$ regret where $K$ denotes the number of episodes. Our work is the first to establish the optimal (w.r.t.~$K$) rate of convergence in the stochastic setting with bandit feedback using a policy optimization based approach, and the first to establish the optimal (w.r.t.~$K$) rate in the adversarial setup with full information feedback, for which no algorithm with an optimal rate guarantee is currently known.