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Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates
Computational Optimization and Applications ( IF 2.2 ) Pub Date : 2021-03-11 , DOI: 10.1007/s10589-020-00249-0
Charles Audet , Kwassi Joseph Dzahini , Michael Kokkolaras , Sébastien Le Digabel

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.



中文翻译:

基于概率估计的随机网格自适应直接搜索用于黑箱优化

我们提出了最初为确定性黑盒优化而开发的网格自适应直接搜索(MADS)算法的随机扩展。称为StoMADS的算法考虑了目标函数f的无约束优化,该目标函数的值只能通过遵循未知分布的随机噪声破坏的黑盒来计算。所提出的方法基于类似于MADS的算法框架,并使用从随机观测值获得的函数值的随机估计值,因为f的确切确定性可计算版本不可用。这样的估计需要以足够大但固定的概率来准确并且满足方差条件。然后,使用mar理论利用拟议算法生成渐近密集的搜索方向集的能力,以证明概率为1时收敛到f的Clarke平稳点。

更新日期:2021-03-11
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