We consider the problem of optimizing functions corrupted with additive noise. It is known that Evolutionary Algorithms can reach a Simple Regret O(1/ √ n) within logarithmic factors, when n is the number of function evaluations. Here, Simple Regret at evaluation n is the difference between the evaluation of the function at the current recommendation point of the algorithm and at the real optimum. We show mathematically that this bound is tight, for any family of functions that includes sphere functions, at least for a wide set of Evolution Strategies without large mutations.

Abstract. Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of algorithms is a set of algorithms equipped with an algorithm selection tool for distributing the computational power among them. We study portfolios of noisy optimization solvers, show that different settings lead to different performances, obtain mathematically proved performance (in the sense that the portfolio performs nearly as well as the best of its algorithms) by an ad hoc selection algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag; i.e., recommend the current recommendation of the best solver, selected from a comparison based on their recommendations earlier in the run.