用神经网络从噪声样本中迭代优化，找全局最小值。
Neural Global Optimization via Iterative Refinement from Noisy Samples
- 输入噪声函数值与样条拟合，通过迭代改进初始猜测。
- 在多峰测试函数上误差仅8.05%，优于初始样条36.24%。
- 无需导数信息或多次重启，适合复杂黑箱优化任务。
从噪声样本中进行黑箱函数的全局优化是机器学习与科学计算中的基础挑战。传统贝叶斯优化常陷入局部极小值，而无梯度方法需大量函数评估。本文提出一种新型神经方法，通过迭代精炼学习寻找全局最小值。模型以噪声函数样本及其拟合样条表示为输入，逐步优化初始猜测至真实全局最小值。在随机生成、通过穷举搜索获得真值的多峰函数上训练，该方法在测试集上平均误差为8.05%，相较样条初始化的36.24%提升28.18%。72%的测试案例误差低于10%，表明其学习的是优化原理而非单纯曲线拟合。架构融合函数值、导数与样条系数等多模态信息，并通过迭代位置更新实现鲁棒全局优化，无需导数信息或多次重启。
原文摘要 · Abstract (English)
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.
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