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

• URL: http://arxiv.org/abs/2402.15171v4
• Date: Fri, 15 Nov 2024 09:41:26 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:
• 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 OLS-UCB-C and COS-V (only the variances for the latter). They both yields improved gap-free regret. Although COS-V can be slightly suboptimal, it improves on computational complexity by taking inspiration from ThompsonSampling approaches. It is the first sampling-based algorithm satisfying a T^1/2 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 >> d but also when P <= d, which is not covered by existing analyses.

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