AI 中文总结
针对含噪声无导数优化问题，提出方向自适应进化策略DAES，通过结构化方向生成机制替代矩阵自适应，建立复杂度界并进行数值实验，为含噪声MAES型无导数方法提供首个高概率复杂度保证，在评估效率和鲁棒性间取得良好平衡。
AI 中文摘要
本文针对含噪声无导数优化问题，开发了一种方向自适应进化策略（DAES），这是一种新型的基于MAES的方法，旨在将进化策略的基于种群的搜索机制与严格的复杂度分析相结合。与标准MAES方案不同，DAES将自适应矩阵固定为单位矩阵，并通过基于对称采样、噪声函数值的联合排序选择、三组重组和新的三角搜索方向的结构化方向生成机制来替代矩阵自适应。具体而言，沿正负配对方向对候选点进行采样，对其不精确函数值进行联合排序，重新排序后的方向被分为三组以构建三个重组点，其几何形状定义了三角方向。然后沿此方向应用有符号充分下降搜索和外推机制。这种结构产生了一种基于种群的MAES型算法，在噪声评估下既保持了有竞争力的实际性能，又便于进行非渐近分析。我们为非凸、凸和强凸目标函数建立了高概率复杂度界，并在噪声限制精度水平上得出了相应的保证。据我们所知，这些结果为具有这种方向自适应结构的含噪声MAES型无导数方法提供了首个高概率复杂度保证。最后，在来自BARON集合的655个prince测试问题上的数值实验将DAES与先进的MAES型求解器MADFO进行了比较，结果表明在评估效率和最终鲁棒性之间取得了良好的平衡。
英文摘要
In this paper, we develop a direction adaptation evolution strategy (DAES) -- a new MAES-type method -- for noisy derivative-free optimization, designed to reconcile the population-based search mechanisms of evolution strategies with rigorous complexity analysis. Unlike standard MAES schemes, DAES fixes the adaptation matrix to the identity and replaces matrix adaptation with a structured direction-generation mechanism based on symmetric sampling, joint sorting-selection of noisy function values, three-group recombination, and a new triangular search direction. Specifically, candidates are sampled along paired positive and negative directions, their inexact function values are jointly ranked, and the reordered directions are partitioned into three groups to construct three recombination points whose geometry defines the triangular direction. A signed sufficient-decrease search and extrapolation mechanism is then applied along this direction. This structure yields a population-based MAES-type algorithm that retains competitive practical behavior while being amenable to nonasymptotic analysis under noisy evaluations. We establish high-probability complexity bounds for nonconvex, convex, and strongly convex objective functions and derive corresponding guarantees at the noise-limited accuracy level. To the best of our knowledge, these results provide the first high-probability complexity guarantees for a noisy MAES-type derivative-free method with this direction-adaptation structure. Finally, numerical experiments on the 655 prince test problems from the BARON collection compare DAES with the advanced MAES-type solver MADFO and show a favorable trade-off between evaluation efficiency and ultimate robustness.
Comments52 pages; 5 figures
