A research paper on Bayesian optimization by authors including Mr. Iwasaki from the MI-6 Ltd. Research Team has been accepted for the prestigious international conference ICML 2026. This study focuses on regret bounds, which measure the theoretical performance of Gaussian Process Thompson Sampling (GP-TS).
While GP-TS is highly effective in practical applications of Bayesian optimization, its theoretical analysis, such as the probabilistic evaluation of cumulative regret, has historically been limited to expected regret, compared to the Gaussian Process Upper Confidence Bound (GP-UCB) method. Furthermore, recent advancements in GP-UCB have introduced performance metrics, called "lenient regret" (which measures losses exceeding a pre-defined tolerance level), and methods to improve the upper bounds of cumulative regret relative to the number of time steps. Whether these advanced analytical techniques could be successfully applied to GP-TS had yet to be determined.
This study successfully addresses these gaps by achieving (1) enhanced probabilistic guarantees, (2) performance guarantees for lenient regret, and (3) improved cumulative regret upper bounds with respect to the number of time steps for GP-TS. Moving forward, the continuous development roadmap will focus on further theoretical optimization, including expanding the scope of the underlying assumptions and extending the applicability of the kernel functions utilized in this analytical framework.
The advancements in mathematical theory by this paper are highly anticipated to contribute to the field of advanced materials development and autonomous experimental optimization, enabling the selection of more reliable optimization algorithms and significantly enhancing exploration efficiency.
Paper Information
- Title: On Regret Bounds of Thompson Sampling for Bayesian Optimization（Link）
- Accepted to：Forty-Third International Conference on Machine Learning (ICML 2026)
- DOI: https://doi.org/10.48550/arXiv.2603.09276
- Authors: ※Affiliations are based on the information at the time of publication.
- Shion Takeno (Nagoya University)
- Shogo Iwazaki (MI-6 Ltd.)
