We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on an algorithmic framework similar to that of MADS and uses random estimates of function values obtained from stochastic observations since the exact deterministic computable version of f is not available. Such estimates are required to be accurate with a sufficiently large but fixed probability and to satisfy a variance condition. The ability of the proposed algorithm to generate an asymptotically dense set of search directions is then exploited using martingale theory to prove convergence to a Clarke stationary point of f with probability one.
Computational Optimization and Applications, 79(1), 1-34, 2021. Doi: 10.1007/s10589-020-00249-0