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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

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

Résumé

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 Thompson Sampling 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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Dates et versions

hal-04470568 , version 1 (22-02-2024)
hal-04470568 , version 2 (02-07-2024)

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Julien Zhou, Pierre Gaillard, Thibaud Rahier, Houssam Zenati, Julyan Arbel. Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits. 2024. ⟨hal-04470568v2⟩
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