Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits

• URL: http://arxiv.org/abs/2402.15171v2
• Date: Wed, 3 Jul 2024 14:29:43 GMT
• Title: Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits
• Authors: Julien Zhou, Pierre Gaillard, Thibaud Rahier, Houssam Zenati, Julyan Arbel,
• Abstract summary: We address the problem of semi-bandits, where a player selects among $P$ actions from the power set of a set containing $d$ base items. We show that our approach efficiently leverages the semi-bandit feedback and outperforms bandit feedback approaches.
• Score: 12.674929126684528
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We address the problem of stochastic combinatorial semi-bandits, where a player selects among $P$ actions from the power set of a set containing $d$ base items. Adaptivity to the problem's structure is essential in order to obtain optimal regret upper bounds. As estimating the coefficients of a covariance matrix can be manageable in practice, leveraging them should improve the regret. We design ``optimistic'' covariance-adaptive algorithms relying on online estimations of the covariance structure, called OLSUCBC and COSV (only the variances for the latter). They both yields improved gap-free regret. Although COSV can be slightly suboptimal, it improves on computational complexity by taking inspiration from Thompson Sampling approaches. It is the first sampling-based algorithm satisfying a $\sqrt{T}$ gap-free regret (up to poly-logs). We also show that in some cases, our approach efficiently leverages the semi-bandit feedback and outperforms bandit feedback approaches, not only in exponential regimes where $P\gg d$ but also when $P\leq d$, which is not covered by existing analyses.

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