A Direction Adaptation Evaluation Strategy for Noisy Derivative-Free Optimization

Morteza Kimiaei; Mahsa Yousefi

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arXiv · 2607.10416

A Direction Adaptation Evaluation Strategy for Noisy Derivative-Free Optimization

Morteza Kimiaei·Mahsa Yousefi

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Abstract

In this paper, we develop a direction adaptation evolution strategy (DAES) -- a new MAES-type method -- for noisy derivative-free optimization, designed to reconcile the population-based search mechanisms of evolution strategies with rigorous complexity analysis. Unlike standard MAES schemes, DAES fixes the adaptation matrix to the identity and replaces matrix adaptation with a structured direction-generation mechanism based on symmetric sampling, joint sorting-selection of noisy function values, three-group recombination, and a new triangular search direction. Specifically, candidates are sampled along paired positive and negative directions, their inexact function values are jointly ranked, and the reordered directions are partitioned into three groups to construct three recombination points whose geometry defines the triangular direction. A signed sufficient-decrease search and extrapolation mechanism is then applied along this direction. This structure yields a population-based MAES-type algorithm that retains competitive practical behavior while being amenable to nonasymptotic analysis under noisy evaluations. We establish high-probability complexity bounds for nonconvex, convex, and strongly convex objective functions and derive corresponding guarantees at the noise-limited accuracy level. To the best of our knowledge, these results provide the first high-probability complexity guarantees for a noisy MAES-type derivative-free method with this direction-adaptation structure. Finally, numerical experiments on the 655 prince test problems from the BARON collection compare DAES with the advanced MAES-type solver MADFO and show a favorable trade-off between evaluation efficiency and ultimate robustness.

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BibTeX RIS

Morteza Kimiaei, Mahsa Yousefi. 2026-07-11. A Direction Adaptation Evaluation Strategy for Noisy Derivative-Free Optimization. https://arxiv.org/abs/2607.10416

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