2024/01/25 by Daiki Morinaga, Morinaga, Daiki, Youhei Akimoto +1
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.2401.14014
openalex publication_date 2024/01/25 · openalex created_date 2024/01/27 · openalex updated_date 2026/07/28
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.