arXiv Machine Learning September 7, 2026 By Mingjie Hu, Jian-Qiang Hu, Enlu Zhou

Optimal Data Acquisition for Reinforcement Learning: A Large Deviations Perspective

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The paper presents a large deviations framework for efficient data acquisition in infinite-horizon reinforcement learning, introducing the exponential decay rate of policy-selection error probability as a key efficiency metric. It derives a variational characterization leading to a nested optimization problem, then proposes a tractable convex relaxation and a lazy one-step projected subgradient method to construct an adaptive data acquisition policy. The resulting algorithm is shown to be near-robustly optimal under the proposed criterion, with extensions to linear function approximation and supporting numerical experiments.

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