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StoMADS: Stochastic blackbox optimization using probabilistic estimates

Charles AUDET (charles.audet***at***gerad.ca)
Kwassi Joseph DZAHINI(kwassi-joseph.dzahini***at***polymtl.ca)
Michael KOKKOLARAS(michael.kokkolaras***at***mcgill.ca)
Sébastien Le DIGABEL(sebastien.le.digabel***at***gerad.ca)

Abstract: This work introduces StoMADS, a stochastic variant of the mesh adaptive direct-search (MADS) algorithm originally developed for deterministic blackbox optimization. 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 satisfy a variance condition. The ability of the proposed algorithm to generate an asymptotically dense set of search directions is then exploited to show convergence to a Clarke stationary point of f with probability one, using martingale theory.

Keywords: Blackbox optimization, Derivative-free optimization, Stochastic optimization, Mesh adaptive direct-search, Probabilistic estimates

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Category 3: Other Topics


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Entry Submitted: 10/02/2019
Entry Accepted: 10/02/2019
Entry Last Modified: 10/02/2019

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