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This work introduces StoMADS, a stochastic variant of the mesh adaptivedirect-search (MADS) algorithm originally developed for deterministic blackboxoptimization. StoMADS considers the unconstrained optimization of an objectivefunction f whose values can be computed only through a blackbox corrupted bysome random noise following an unknown distribution. The proposed method isbased on an algorithmic framework similar to that of MADS and uses randomestimates of function values obtained from stochastic observations since theexact deterministic computable version of f is not available. Such estimatesare required to be accurate with a sufficiently large but fixed probability andsatisfy a variance condition. The ability of the proposed algorithm to generatean asymptotically dense set of search directions is then exploited to showconvergence to a Clarke stationary point of f with probability one, usingmartingale theory.

StoMADS: Stochastic blackbox optimization using probabilistic estimates