Optimism in Reinforcement Learning with Generalized Linear Function Approximation

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 O(d^3 T) where 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.

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