אופטימיזציה חסרת פרמטרים ללא-מספרי: דגימה אליפסית

תקציר מקורי באנגליתarXiv:2609.38561v2 Announce Type: replace-cross Abstract: Zeroth-order optimization methods are essential for solving black-box problems where gradient information is unavailable or expensive to compute. This paper presents POEM-ES, a novel parameter-free stochastic zeroth-order algorithm that extends the recent POEM method by integrating subspace preconditioning with ellipsoidal randomized sampling. In contrast to traditional zeroth-order approaches that rely on isotropic random directions, POEM-ES performs anisotropic sampling guided by a fixed structural symmetric positive semi-definite (SPSD) preconditioner $\hat{\Sigma}$ that encodes the underlying low-dimensional geometry. Under a standard structural spectral normalization where $\lambda_{\max}(\hat{\Sigma}) = 1$, we introduce the us