Parameter Tuning by Simple Regret Algorithms and Multiple Simultaneous Hypothesis Testing

Simple regret" algorithms are designed for noisy optimization in unstructured domains. In particular, this literature has shown that the uniform algorithm is indeed optimal asymptotic ally and suboptimal non- asymptotically. We investigate theoretically and experimentally the application of these algorithms, for auto- matic parameter tuning, in particular from the point of view of the number of samples required for "uniform" to be relevant and from the point of view of statistical guarantees. We see that for moderate numbers of arms, the possible improvement in terms of computational power required for statistical validation can't be more than linear as a function of the number of arms and provide a simple rule to check if the simple uniform al- gorithm (trivially parallel) is relevant. Our experiments are performed on the tuning of a Monte-Carlo Tree Search algorithm, a great recent tool for high-dimensional planning with particularly impressive results for difficult games and in particular the game of Go.