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arXiv · 2110.09133

Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits

Reda Ouhamma·Rémy Degenne·Pierre Gaillard·Vianney Perchet
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Abstract

In the fixed budget thresholding bandit problem, an algorithm sequentially allocates a budgeted number of samples to different distributions. It then predicts whether the mean of each distribution is larger or lower than a given threshold. We introduce a large family of algorithms (containing most existing relevant ones), inspired by the Frank-Wolfe algorithm, and provide a thorough yet generic analysis of their performance. This allowed us to construct new explicit algorithms, for a broad class of problems, whose losses are within a small constant factor of the non-adaptive oracle ones. Quite interestingly, we observed that adaptive methods empirically greatly out-perform non-adaptive oracles, an uncommon behavior in standard online learning settings, such as regret minimization. We explain this surprising phenomenon on an insightful toy problem.

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Reda Ouhamma, Rémy Degenne, Pierre Gaillard, Vianney Perchet. 2021-10-18. Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits. https://arxiv.org/abs/2110.09133

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