Poster
Towards Efficient and Optimal Covariance-Adaptive Algorithms for Combinatorial Semi-Bandits
Julien Zhou · Pierre Gaillard · Thibaud Rahier · Houssam Zenati · Julyan Arbel
West Ballroom A-D #5809
Abstract:
We address the problem of stochastic combinatorial semi-bandits, where a player selects among actions from the power set of a set containing 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 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 but also when , which is not covered by existing analyses.
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