arXiv Machine Learning June 11, 2026 By Shion Takeno, Shogo Iwazaki

On Regret Bounds of Thompson Sampling for Bayesian Optimization

Read the original on arXiv Machine Learning →

arXiv:2603. 09276v2 Announce Type: replace-cross Abstract: We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

Aug 18

Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization

arXiv:2608. 16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization.

By Shion Takeno, Shogo Iwazaki

reinforcement-learning

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)

reinforcement-learning

arXiv Machine Learning

Jun 9

Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling

arXiv:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.

By Jack Sandberg, Morteza Haghir Chehreghani

arXiv Machine Learning

Aug 20

Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration

arXiv:2608. 18863v1 Announce Type: cross Abstract: We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model.

By Matthias Mandl, Hanne Kekkonen

arXiv Machine Learning

Sep 3

Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling

arXiv:2609. 01999v1 Announce Type: cross Abstract: We study a variant of the Thompson Sampling (TS) algorithm, called $\alpha$-TS, for solving stochastic generalized linear bandit problems.

By Prateek Jaiswal, Debdeep Pati, Anirban Bhattacharya, Bani K. Mallick

reinforcement-learning

arXiv Machine Learning

Jun 24

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

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

By Hamish Flynn, Joe Watson, Ingmar Posner, Jan Peters

reinforcement-learning

One email a morning, machine-written

Related stories

Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization

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

Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling

Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration

Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling

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