Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates
Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates
复制标题
使用渐进障碍和概率估计的约束随机黑盒优化
DOI：
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发表时间：
2020
影响因子：
2.7
通讯作者：
Sébastien Le Digabel
中科院分区：
文献类型：
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作者：
K. J. Dzahini;M. Kokkolaras;Sébastien Le Digabel
这项工作介绍了StoMADS-PB算法的约束随机黑箱优化，这是一个扩展的网格自适应直接搜索（MADS）方法最初开发的确定性黑箱优化一般约束条件下。目标和约束函数的值由噪声黑盒提供，即，它们只能用分布未知的随机噪声来计算。与MADS中一样，约束违反被聚合到单个约束违反函数中。由于所有函数值在数值上都不可用，StoMADS-PB使用估计值并为违规引入概率界限。从随机观测中获得的这种估计和界限要求是准确和可靠的，具有很高的，但固定的概率。所提出的方法，它允许中间不可行的解决方案，接受新的点，使用充分的减少条件和施加阈值的概率界限。利用Clarke非光滑微积分和鞅理论，得到了目标函数和破坏函数的概率为1的Clarke平稳收敛结果.
This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. As in MADS, constraint violations are aggregated into a single constraint violation function. Since all function values are numerically unavailable, StoMADS-PB uses estimates and introduces probabilistic bounds for the violation. Such estimates and bounds obtained from stochastic observations are required to be accurate and reliable with high, but fixed, probabilities. The proposed method, which allows intermediate infeasible solutions, accepts new points using sufficient decrease conditions and imposing a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one.