Optimism in reinforcement learning with generalized linear function approximation

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 \tilde{O}(\sqrt{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.