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：本文提出了一种新的全局优化启发式方法，适用于代价函数评估昂贵、难以获取甚至不可行的场景。该方法被命名为"景观-勾勒-步进（LSS）"，它融合了机器学习、随机优化和强化学习技术，利用先前采样点的历史信息，对需要评估代价函数的参数值进行明智选择。与副本交换蒙特卡洛优化方法不同，该方法所需的代价函数评估次数与模拟退火算法相当，这一特性在高吞吐计算或高性能计算等评估成本高昂或耗时长的场景中尤为重要。该方法也与标准替代优化技术有所区别，因为它不构建旨在近似或重构目标函数的替代模型。我们通过将其应用于低维优化问题（维度为1、2、4和8）来展示该方法，这些问题模拟了凝聚态物理中常见的崎岖能量景观的最小化难题，其中代价函数崎岖不平且充满局部极小值。与经典模拟退火算法相比，LSS方法有效加速了优化过程。