神经方法通过迭代细化从噪声样本中实现全局优化

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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.

Comments:	17 pages, 5 figures, 2 tables
Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:	arXiv:2604.03614 [cs.LG]
	(or arXiv:2604.03614v3 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2604.03614 arXiv-issued DOI via DataCite

Submission history

From: Qusay Muzaffar [view email]
[v1] Sat, 4 Apr 2026 07:02:38 UTC (15 KB)
[v2] Sat, 18 Jul 2026 14:19:09 UTC (39 KB)
[v3] Tue, 6 Oct 2026 15:33:54 UTC (345 KB)