# Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors

arXiv: https://arxiv.org/abs/2602.14472 · HTML: https://mlsanity.com/paper/2602.14472/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Robust Bayesian Optimization via Tempered Posteriors](https://mlsanity.com/paper/2601.07094/) (2026)

## Built on by (most cited first, 1 of 1)

- [Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization](https://mlsanity.com/paper/2610.19925/) (2026)

## Abstract (arXiv)

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 α ∈ (0,1). We derive a kernel-agnostic regret bound expressed in terms of the information gain parameter γt and the posterior contraction rate εt, and identify conditions on the Gaussian process prior under which εt can be controlled. As special cases of our general bound, we recover regret of order tildeO(T^frac12) for the squared exponential kernel, tildeO(T^frac2nu+3d2(2nu+d) ) for the Mat'ern-nu kernel, and a bound of order tildeO(T^frac2nu+3d2(2nu+d)) for the rational quadratic kernel. Overall, our analysis provides a unified and discretization-free regret framework for GP-TS that applies broadly across kernel classes.