Optimal Online Regret for Context-Lumpable Bandits

Abstract: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 identical within a block, one selected arm eliminates all surviving records from that block, requiring at most $r$ selections at each level. Multi-scale exploration assigns finer accuracies to frequent blocks and coarser accuracies to rare blocks, yielding a near-optimal arm for every block while keeping the weighted policy error small.

Machine Learning (cs.LG)

arXiv:2610.18258 [cs.LG]

(or arXiv:2610.18258v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.18258 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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