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 (QUBO) 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, to our knowledge, the first 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.

翻译：组合优化问题在实践应用和优化方法发展中均处于核心地位。尽管经典算法与量子算法经过数十年发展已日趋完善，但机器学习辅助方法相对较新，且尚未能稳定超越简单的最先进经典方法。本文聚焦于一类二次无约束二值优化问题，特别是三维伊辛自旋玻璃中寻找最小能量构型的挑战。我们采用一种全局退火蒙特卡洛算法，该算法将标准局部移动与通过机器学习提出的全局移动相结合。研究表明，局部移动对实现最优性能具有关键作用。通过与模拟退火和群体退火进行基准测试，我们证明全局退火不仅超越了模拟退火的性能，而且展现出比群体退火更强的鲁棒性——无需超参数调整即可在不同问题难度和系统规模下保持有效性。据我们所知，这些结果首次为机器学习辅助优化方法在组合优化场景中超越经典最先进技术的能力提供了明确而坚实的证据。