Optimal Regret for Single Index Bandits
We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function. This model extends linear and generalized linear bandits to a nonparametric setting, and is particularly relevant when the reward function is not known in advance. While optimal regret guarantees are known for monotone reward functions, the general non-monotone case remains poorly understood, with the best known bound being $\tilde{\mathcal{O}}(T^{3/4})$ (under standard boundedness and Lipschitz assumptions on the reward function [Kang et al., 2025]). We close this gap by establishing the optimal regret for gene...
| Authors | Devdan Dey, Sujoy Bhore, Avishek Ghosh |
|---|---|
| Primary category | stat.ML |
| Published | 10 May 2026 |
| Last updated at source | 1 August 2026 |
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