Parameter-Free Zeroth-Order Optimization with Ellipsoidal Sampling
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 $\hatΣ$ that encodes the underlying low-dimensional geometry. Under a standard structural spectral normalization where $λ_{\max}(\hatΣ) ...
| Authors | Alexander Sholokhov, Alexander Rogozin |
|---|---|
| Primary category | math.OC |
| Published | 29 September 2026 |
| Last updated at source | 8 October 2026 |
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