# Statistical efficiency of Thompson sampling for combinatorial semi-bandits

Abstract : We investigate stochastic combinatorial multi-armed bandit with semi-bandit feedback (CMAB). In CMAB, the question of the existence of an efficient policy with an optimal asymptotic regret (up to a factor poly-logarithmic with the action size) is still open for many families of distributions, including mutually independent outcomes, and more generally the multivariate sub-Gaussian family. We propose to answer the above question for these two families by analyzing variants of the Combinatorial Thompson Sampling policy (CTS). For mutually independent outcomes in $[0,1]$, we propose a tight analysis of CTS using Beta priors. We then look at the more general setting of multivariate sub-Gaussian outcomes and propose a tight analysis of CTS using Gaussian priors. This last result gives us an alternative to the Efficient Sampling for Combinatorial Bandit policy (ESCB), which, although optimal, is not computationally efficient.
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Conference papers
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https://hal.inria.fr/hal-03288983
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Submitted on : Friday, July 16, 2021 - 3:55:03 PM
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richemond2020byol.pdf
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### Identifiers

• HAL Id : hal-03288983, version 1
• ARXIV : 2006.06613

### Citation

Pierre H Richemond, Jean-Bastien Grill, Florent Altché, Corentin Tallec, Florian Strub, et al.. Statistical efficiency of Thompson sampling for combinatorial semi-bandits. Neural Information Processing Systems Conference, Dec 2020, Virtual, France. ⟨hal-03288983⟩

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