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This research introduces a neural architecture designed to solve global optimization problems for black-box functions using noisy samples, offering significant improvements over traditional Bayesian Optimization and gradient-free methods. By iteratively refining initial guesses through learned principles rather than simple curve fitting, the model effectively avoids local minima in multi-modal landscapes without requiring derivative information or multiple restarts. The approach represents a notable advancement in machine learning techniques applicable to scientific computing where function evaluations are costly or noisy.
Neural Global Optimization via Iterative Refinement from Noisy Samples
arXiv:2604.03614v2 Announce Type: replace-cross Abstract: Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal functions, while gradient-free methods require many function evaluations. We present a novel neural approach that learns to find global minima through iterative refinement. Our model takes noisy function samples and their fitted spline representation as input, then iteratively refines an initial guess toward the true global minimum. Trained on randomly generated functions with ground truth global minima obtained via exhaustive search, our method achieves a mean error of 8.05 percent on challenging multi-modal test functions, compared to 36.24 percent for the spline initialization, a 28.18 percent improvement. The model successfully finds global minima in 72 percent of test cases with error below 10 percent, demonstrating learned optimization principles rather than mere curve fitting. Our architecture combines encoding of multiple modalities including function values, derivatives, and spline coefficients with iterative position updates, enabling robust global optimization without requiring derivative information or multiple restarts.
Abstract:Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal functions, while gradient-free methods require many function evaluations. We present a novel neural approach that learns to find global minima through iterative refinement. Our model takes noisy function samples and their fitted spline representation as input, then iteratively refines an initial guess toward the true global minimum. Trained on randomly generated functions with ground truth global minima obtained via exhaustive search, our method achieves a mean error of 8.05 percent on challenging multi-modal test functions, compared to 36.24 percent for the spline initialization, a 28.18 percent improvement. The model successfully finds global minima in 72 percent of test cases with error below 10 percent, demonstrating learned optimization principles rather than mere curve fitting. Our architecture combines encoding of multiple modalities including function values, derivatives, and spline coefficients with iterative position updates, enabling robust global optimization without requiring derivative information or multiple restarts.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2604.03614 [cs.LG]
(or arXiv:2604.03614v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.03614 Focus to learn more arXiv-issued DOI via DataCite
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