## Optimism in Reinforcement Learning with Generalized Linear Function Approximation

### Yining Wang · Ruosong Wang · Simon Du · Akshay Krishnamurthy

Keywords: [ reinforcement learning ] [ exploration ] [ function approximation ] [ theory ] [ optimism ] [ regret analysis ] [ provable sample efficiency ]

[ Abstract ]
[ Paper ]
Wed 5 May 9 a.m. PDT — 11 a.m. PDT

Abstract: We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call optimistic closure,'' which is strictly weaker than assumptions from prior analyses for the linear setting. With optimistic closure, we prove that our algorithm enjoys a regret bound of $\widetilde{O}\left(H\sqrt{d^3 T}\right)$ where $H$ is the horizon, $d$ is the dimensionality of the state-action features and $T$ is the number of episodes. This is the first statistically and computationally efficient algorithm for reinforcement learning with generalized linear functions.