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.
Published April 2019 , 27 pages
This cahier was revised in October 2019