Neural Global Optimization via Iterative Refinement from Noisy Samples

TL;DR

This paper introduces a neural network-based method for global optimization that iteratively refines guesses from noisy samples, outperforming traditional approaches on multi-modal functions.

Contribution

A novel neural approach that learns to find global minima through iterative refinement, using a model trained on synthetic functions to improve optimization accuracy.

Findings

Achieves 8.05% mean error on challenging functions, significantly better than 36.24% for initialization.

Successfully finds global minima in 72% of test cases with error below 10%.

Combines encoding of function values, derivatives, and spline coefficients for robust optimization.

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.