Efficient Best-of-Both-Worlds Algorithms for Contextual Combinatorial Semi-Bandits

• URL: http://arxiv.org/abs/2508.18768v1
• Date: Tue, 26 Aug 2025 07:51:22 GMT
• Title: Efficient Best-of-Both-Worlds Algorithms for Contextual Combinatorial Semi-Bandits
• Authors: Mengmeng Li, Philipp Schneider, Jelisaveta Aleksić, Daniel Kuhn,
• Abstract summary: We introduce the first best-of-both-worlds algorithm for contextual semi-bandits that simultaneously guarantees $widetildemathcalO(sqrtT)$ regret.<n>By leveraging the Karush-Kuhn-Tucker conditions, we transform the $K$ convex projection problem into a single-dimensional root-finding problem.<n> Empirical evaluations demonstrate that this combined strategy not only attains the attractive regret bounds of best-of-both-worlds algorithms but also delivers substantial per-round speed-ups.
• Score: 3.448177863267093
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the first best-of-both-worlds algorithm for contextual combinatorial semi-bandits that simultaneously guarantees $\widetilde{\mathcal{O}}(\sqrt{T})$ regret in the adversarial regime and $\widetilde{\mathcal{O}}(\ln T)$ regret in the corrupted stochastic regime. Our approach builds on the Follow-the-Regularized-Leader (FTRL) framework equipped with a Shannon entropy regularizer, yielding a flexible method that admits efficient implementations. Beyond regret bounds, we tackle the practical bottleneck in FTRL (or, equivalently, Online Stochastic Mirror Descent) arising from the high-dimensional projection step encountered in each round of interaction. By leveraging the Karush-Kuhn-Tucker conditions, we transform the $K$-dimensional convex projection problem into a single-variable root-finding problem, dramatically accelerating each round. Empirical evaluations demonstrate that this combined strategy not only attains the attractive regret bounds of best-of-both-worlds algorithms but also delivers substantial per-round speed-ups, making it well-suited for large-scale, real-time applications.

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