In black-box optimization, noise in the objective function is inevitable. Noise disrupts the ranking of candidate solutions in comparison-based optimization, possibly deteriorating the search performance compared with a noiseless scenario. Explicit averaging takes the sample average of noisy objective function values and is widely used as a simple and versatile noise-handling technique. Although it is suitable for various applications, it is ineffective if the mean is not finite. We theoretically reveal that explicit averaging has a negative effect on the estimation of ground-truth rankings when assuming stably distributed noise without a finite mean. Alternatively, sign averaging is proposed as a simple but robust noise-handling technique. We theoretically prove that the sign averaging estimates the order of the medians of the noisy objective function values of a pair of points with arbitrarily high probability as the number of samples increases. Its advantages over explicit averaging and its robustness are also confirmed through numerical experiments.

翻译：在黑箱优化中，目标函数的噪声是不可避免的。噪声会干扰基于比较优化中候选解的排序，可能比无噪声场景下更严重地恶化搜索性能。显式平均通过对含噪目标函数值进行样本平均，作为一种简单通用的噪声处理技术被广泛使用。尽管该方法适用于多种应用场景，但当均值不存在时则无效。我们理论上揭示了：在假设噪声服从无有限均值的稳定分布时，显式平均对真实排序的估计会产生负面影响。为此，我们提出符号平均作为简单但鲁棒的噪声处理技术。我们从理论上证明：随着样本数量增加，符号平均能以任意高概率估计出一对点中含噪目标函数值的中位数顺序。通过数值实验，我们进一步确认了该方法相对于显式平均的优势及其鲁棒性。