Optimistically Optimistic Exploration for Provably Efficient Infinite-Horizon Reinforcement and Imitation Learning

• URL: http://arxiv.org/abs/2502.13900v1
• Date: Wed, 19 Feb 2025 17:32:35 GMT
• Title: Optimistically Optimistic Exploration for Provably Efficient Infinite-Horizon Reinforcement and Imitation Learning
• Authors: Antoine Moulin, Gergely Neu, Luca Viano,
• Abstract summary: We propose the first computationally efficient algorithm achieving near-optimal regret guarantees in infinite-horizon discounted linear Markov decision processes. We show that, combined with a regularized approximate dynamic-programming scheme, the resulting algorithm achieves a regret of order $tildemathcalO (sqrtd3 (1 - gamma)- 7 / 2 T)$, where $T$ is the total number of sample transitions, $gamma in (0,1)$ is the discount factor, and $d$ is the feature dimensionality.
• Score: 13.429541377715296
• License:
• 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 near-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.

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