A General $\widetildeΩ(\sqrt{T γ_T})$ Lower Bound for Kernel Bandits
The kernel bandit problem consists of sequentially optimizing an unknown function with noisy feedback, where the function has bounded norm in a given Reproducing Kernel Hilbert Space (RKHS). A central quantity in the regret analysis of kernel bandits is the maximum information gain $γ_T$. In particular, the best existing upper bounds scale as $\sqrt{Tγ_T}$ up to log factors, and nearly-matching lower bounds have been derived for specific kernels such as squared exponential and Matérn. However, lower bounds for general kernels are lacking, thus making it unclear in what generality the upper bounds are near-optimal. In this paper, we establish a general $Ω(\sqrt{Tγ_T/\log T})$ minimax regre...
| Authors | Chenkai Ma, Jonathan Scarlett |
|---|---|
| Primary category | stat.ML |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
Popularity, last 2 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.