Demonstrating real advantage of machine learning–enhanced Monte Carlo for combinatorial optimization

Abstract

Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning–assisted approaches are comparatively recent and have not yet consistently outperformed simple, state-of-the-art classical methods. Here, we focus on a class of Quadratic Unconstrained Binary Optimization problems, specifically the challenge of finding minimum energy configurations in three-dimensional Ising spin glasses. We use a Global Annealing Monte Carlo algorithm that integrates standard local moves with global moves proposed via machine learning. We show that local moves play a crucial role in achieving optimal performance. Benchmarking against Simulated Annealing and Population Annealing, we demonstrate that Global Annealing not only surpasses the performance of Simulated Annealing but also exhibits greater robustness than Population Annealing, maintaining effectiveness across problem hardness and system size without hyperparameter tuning. These results provide clear and robust evidence that a machine learning–assisted optimization method can exceed the capabilities of classical state-of-the-art techniques in a combinatorial optimization setting.