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.

翻译：本文提出了一种针对全局优化的新启发式方法，适用于目标函数评估成本高昂、难以获取甚至无法进行大规模评估的场景。该方法名为"景观草图步进"（Landscape-Sketch-and-Step, LSS），融合了机器学习、随机优化和强化学习技术，通过利用历史采样点的信息，明智地选择目标函数应被评估的参数值。与副本交换蒙特卡洛优化方法不同，本方法所需的目标函数评估次数与模拟退火相当，这一特性在诸如高通量计算或高性能计算任务等评估成本高或耗时长的情况下尤为重要。该方法也不同于标准的替代优化技术，因为它不构建旨在近似或重构目标函数的替代模型。我们将该方法应用于低维优化问题（维度1、2、4、8），这些问题模拟了凝聚态物理中常见的崎岖能量景观上的最小化困难，其中目标函数崎岖不平且充满局部极小值。与经典模拟退火相比，LSS展现出对优化过程的有效加速。