@inproceedings{
zhou2024towards,
title={Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits},
author={Julien Zhou and Pierre Gaillard and Thibaud Rahier and Houssam Zenati and Julyan Arbel},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=PI0CDY6nmo}
}
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 $\sqrt{T}$ 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.
Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits
Julien Zhou Pierre Gaillard Thibaud Rahier Houssam Zenati Julyan Arbel