Title: GLENS: Global Search via Learning from Solver Iterates with Diffusion Models

Abstract

This study addresses the challenge of producing a substantial set of initial guesses for locating local minima in multimodal, non-convex, continuous optimization tasks. The primary objective is to ensure these starting points are both high-quality—facilitating rapid convergence by numerical solvers—and diverse, thereby representing a wide array of distinct local minima. While identifying multiple locally optimal solutions supports more flexible downstream decision-making, it traditionally demands costly global search procedures. Current data-driven approaches typically rely solely on the final converged optima from offline solver executions to predict initial guesses. This limitation discards valuable information regarding the local neighborhoods of solutions and restricts the volume of available training data.

To overcome these constraints, we introduce GLENS (Global Search via Learning from Solver Iterates), a data-efficient global search framework that utilizes intermediate solver iterates as a form of free data augmentation. GLENS comprises two distinct modules: a neighborhood structure model, which employs diffusion models to capture the local geometry surrounding optima based on problem parameters, and a solver behavior model, which learns refinement directions to steer samples toward nearby optima during the diffusion sampling process.

Our experiments, conducted on modified non-convex benchmark problems as well as a two-robot obstacle-avoidance navigation scenario, demonstrate that GLENS successfully generates high-quality initial guesses while maintaining the multimodal distribution of diverse local optima. These resulting initial guesses facilitate faster solver convergence across various problem configurations and different solver types. Additionally, we provide an analysis of how specific hyperparameter selections influence overall performance.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC