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Oracle-Efficient Combinatorial Semi-Bandits
[Submitted on 24 Oct 2025 (v1), last revised 11 Jul 2026 (this v · 2025-10-24 · via stat updates on arXiv.org

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Abstract:We study the combinatorial semi-bandit problem where an agent selects a subset of base arms and receives individual feedback. While this generalizes the classical multi-armed bandit and has broad applicability, its scalability is limited by the high cost of combinatorial optimization, requiring oracle queries at every round. To tackle this, we propose oracle-efficient frameworks that significantly reduce oracle calls while maintaining tight regret guarantees. For the worst-case linear reward setting, our algorithms achieve $\tilde{O}(\sqrt{T})$ regret using only $O(\log\log T)$ oracle queries. We also propose covariance-adaptive algorithms that leverage noise structure for improved regret, and extend our approach to general (non-linear) rewards. Overall, our methods reduce oracle usage from linear to (doubly) logarithmic in time, with strong theoretical guarantees.

Submission history

From: Jung-Hun Kim [view email]
[v1] Fri, 24 Oct 2025 13:07:08 UTC (216 KB)
[v2] Sat, 11 Jul 2026 17:20:16 UTC (214 KB)