Nearly Minimax Optimal Regret for Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation
This provides a foundational advance for RL researchers by establishing the first nearly optimal algorithm in this setting, addressing a key theoretical bottleneck.
The paper tackles reinforcement learning in infinite-horizon average-reward MDPs with linear function approximation by proposing the UCRL2-VTR algorithm, achieving a regret of $ ilde{O}(d\sqrt{DT})$ and proving a matching lower bound, making it nearly minimax optimal.
We study reinforcement learning in an infinite-horizon average-reward setting with linear function approximation, where the transition probability function of the underlying Markov Decision Process (MDP) admits a linear form over a feature mapping of the current state, action, and next state. We propose a new algorithm UCRL2-VTR, which can be seen as an extension of the UCRL2 algorithm with linear function approximation. We show that UCRL2-VTR with Bernstein-type bonus can achieve a regret of $\tilde{O}(d\sqrt{DT})$, where $d$ is the dimension of the feature mapping, $T$ is the horizon, and $\sqrt{D}$ is the diameter of the MDP. We also prove a matching lower bound $\tildeΩ(d\sqrt{DT})$, which suggests that the proposed UCRL2-VTR is minimax optimal up to logarithmic factors. To the best of our knowledge, our algorithm is the first nearly minimax optimal RL algorithm with function approximation in the infinite-horizon average-reward setting.