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

• URL: http://arxiv.org/abs/2110.09133v1
• Date: Mon, 18 Oct 2021 09:36:36 GMT
• Title: Online Sign Identification: Minimization of the Number of Errors in Thresholding Bandits
• Authors: Reda Ouhamma, R\'emy Degenne, Pierre Gaillard, Vianney Perchet
• Abstract summary: We introduce a large family of algorithms inspired by the Frank-Wolfe algorithm. We construct new explicit algorithms for a broad class of problems. We explain this phenomenon on an insightful toy problem.
• Score: 27.09804256642197
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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