2024/09/25 by Catalin-Viorel Dinu, Dinu, Catalin-Viorel, Yash J. Patel +5 · 1 citation
Computer Science · #Advanced Multi-Objective Optimization Algorithms #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.2409.16757
openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound of the expected improvement achieved in one iteration of CMA-ES, given an estimation of the noise level and the Lipschitz constant of the function's gradient. Solving for the maximum of the lower bound, we obtain a simple expression of the optimal re-evaluation number. We experimentally compare our method to the state-of-the-art noise-handling methods for CMA-ES on a set of artificial test functions across various noise levels, optimization budgets, and dimensionality. Our method demonstrates significant advantages in terms of the probability of hitting near-optimal function values.