Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization
Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$. We investigate the convergence rates of Gaussian process Thompson sampling (GP-TS) under noiseless observations, assuming a fixed objective function in a reproducing kernel Hilbert space (RKHS). For Matérn kernels with smoothness parameter $ν$ in dimension $d$, we establish a worst-case expected simple-regret upper bound of $O(N^{-ν/d}\sqrt{\log N})$ for both discrete GP-TS on sufficiently fine grids and its continuous counterpart. For the continuous implementation, we develop a nested-grid argument to control posterior sample paths over the entire dom...
| Authors | Haowei Wang, Yilin Zheng |
|---|---|
| Primary category | stat.ML |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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