Optimal Online Regret for Context-Lumpable Bandits
We study stochastic contextual bandits with an unknown context-lumpable structure. The $S$ contexts are partitioned into $r$ blocks, and every arm has the same mean reward across contexts in the same block. Under arbitrary context distributions and without separation assumptions, we design an algorithm with expected regret $\widetilde{O}(\sqrt{r(S+K)T})$, matching the lower bound of Lee et al. (2023) up to logarithmic factors and improving their previous upper bound by a factor of $r$. The algorithm operates over dyadic accuracy levels, using a baseline policy and confidence-based early stopping to control exploration. It then performs cross-context elimination: since rewards are identica...
| Authors | Chenyu Lu, Zihan Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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