  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.
