Abstract

We study the problem of reinforcement learning in infinite-horizon discounted linear Markov decision processes (MDPs), and propose the first computationally efficient algorithm achieving rate-optimal regret guarantees in this setting. Our main idea is to combine two classic techniques for optimistic exploration: additive exploration bonuses applied to the reward function, and artificial transitions made to an absorbing state with maximal return. We show that, combined with a regularized approximate dynamic-programming scheme, the resulting algorithm achieves a regret of order \tilde{\mathcal{O}} (\sqrt{d^{3 (1 – \gamma)}{- 7 / 2} T}), where T is the total number of sample transitions, \gamma \in (0,1) is the discount factor, and d is the feature dimensionality. The results continue to hold against adversarial reward sequences, enabling application of our method to the problem of imitation learning in linear MDPs, where we achieve state-of-the-art results.