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[2602.14472] Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors
Summary
This paper presents a frequentist regret analysis of Gaussian Process Thompson Sampling (GP-TS) using fractional posteriors, offering a unified framework that avoids discretization and provides kernel-agnostic regret bounds.
Why It Matters
The findings enhance the understanding of Gaussian Process Thompson Sampling, a key method in machine learning for decision-making. By providing a framework that is independent of discretization, this research broadens the applicability of GP-TS across various kernel classes, making it significant for both theoretical and practical advancements in the field.
Key Takeaways
- Introduces a novel frequentist regret analysis for GP-TS using fractional posteriors.
- Establishes kernel-agnostic regret bounds applicable across different kernel classes.
- Demonstrates that variance inflation in GP-TS can be interpreted through fractional posteriors.
- Identifies conditions under which the posterior contraction rate can be controlled.
- Recovers known regret bounds for specific kernels as special cases of the general framework.
Mathematics > Statistics Theory arXiv:2602.14472 (math) [Submitted on 16 Feb 2026] Title:Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors Authors:Somjit Roy, Prateek Jaiswal, Anirban Bhattacharya, Debdeep Pati, Bani K. Mallick View a PDF of the paper titled Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors, by Somjit Roy and 4 other authors View PDF Abstract:We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractional Gaussian process posteriors, without relying on domain discretization as in prior work. We show that the variance inflation commonly assumed in existing analyses of GP-TS can be interpreted as Thompson Sampling with respect to a fractional posterior with tempering parameter $\alpha \in (0,1)$. We derive a kernel-agnostic regret bound expressed in terms of the information gain parameter $\gamma_t$ and the posterior contraction rate $\epsilon_t$, and identify conditions on the Gaussian process prior under which $\epsilon_t$ can be controlled. As special cases of our general bound, we recover regret of order $\tilde{\mathcal{O}}(T^{\frac{1}{2}})$ for the squared exponential kernel, $\tilde{\mathcal{O}}(T^{\frac{2\nu+3d}{2(2\nu+d)}} )$ for the Matérn-$\nu$ kernel, and a bound of order $\tilde{\mathcal{O}}(T^{\frac{2\nu+3d}{2(2\nu+d)}})$ for the rational quadr...
