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

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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reda ouhamma, Rémy Degenne, Vianney Perchet, Pierre Gaillard


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 methodsempirically 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.