arXiv Machine Learning By Hamish Flynn, Joe Watson, Ingmar Posner, Jan Peters

Posterior Sampling Reinforcement Learning with Gaussian Processes for Continuous Control: Sublinear Regret Bounds for Unbounded State Spaces

Read the original on arXiv Machine Learning →

arXiv:2603. 08287v2 Announce Type: replace-cross Abstract: We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm.

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arXiv Machine Learning
Sep 25

Exact Bayes Regret and Asymptotic Optimality in High-Dimensional Gaussian Bandits

The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.

By Prakhar Singhvi (Abstract Math Institute), Yi Zou (Abstract Math Institute), Abhishek Bhattacharjee (Abstract Math Institute)