Landscape-Sketch-Step: An AI/ML-Based Metaheuristic for Surrogate Optimization Problems

TL;DR

This paper presents Landscape-Sketch-and-Step (LSS), a novel AI/ML-based metaheuristic for efficient global optimization that reduces the number of costly function evaluations without constructing explicit surrogate models.

Contribution

LSS combines machine learning, stochastic optimization, and reinforcement learning to improve global optimization efficiency, especially in high-cost evaluation scenarios, without surrogate model reconstruction.

Findings

LSS accelerates optimization compared to classical methods.

LSS requires a similar number of evaluations as Simulated Annealing.

LSS effectively handles rugged energy landscapes in low-dimensional problems.

Abstract

In this paper, we introduce a new heuristics for global optimization in scenarios where extensive evaluations of the cost function are expensive, inaccessible, or even prohibitive. The method, which we call Landscape-Sketch-and-Step (LSS), combines Machine Learning, Stochastic Optimization, and Reinforcement Learning techniques, relying on historical information from previously sampled points to make judicious choices of parameter values where the cost function should be evaluated at. Unlike optimization by Replica Exchange Monte Carlo methods, the number of evaluations of the cost function required in this approach is comparable to that used by Simulated Annealing, quality that is especially important in contexts like high-throughput computing or high-performance computing tasks, where evaluations are either computationally expensive or take a long time to be performed. The method also differs from standard Surrogate Optimization techniques, for it does not construct a surrogate model that aims at approximating or reconstructing the objective function. We illustrate our method by applying it to low dimensional optimization problems (dimensions 1, 2, 4, and 8) that mimick known difficulties of minimization on rugged energy landscapes often seen in Condensed Matter Physics, where cost functions are rugged and plagued with local minima. When compared to classical Simulated Annealing, the LSS shows an effective acceleration of the optimization process.