StepDIRECT --一种无导数的阶梯函数最优化方法
StepDIRECT -- A Derivative-Free Optimization Method for Stepwise Functions
摘要：
在本文中，我们提出了StepDIRECT算法的无导数优化（DFO），其中的黑盒目标函数具有阶梯景观。我们的框架是基于著名的直接算法。通过结合局部变异性来探索平坦性，我们提供了一个新的标准来选择潜在的最佳超矩形。此外，我们引入了一个随机局部搜索算法执行潜在的最优超矩形，以提高解决方案的质量和收敛速度。证明了StepDIRECT算法的整体收敛性。随机森林模型的优化和超参数调整的数值实验支持我们的算法的有效性。与其他最先进的基线DFO方法（包括原始DIRECT算法）相比，拟议的StepDIRECT算法显示出具有竞争力的性能结果。
英文摘要：
In this paper, we propose the StepDIRECT algorithm for derivative-free optimization (DFO), in which the black-box objective function has a stepwise landscape. Our framework is based on the well-known DIRECT algorithm. By incorporating the local variability to explore the flatness, we provide a new criterion to select the potentially optimal hyper-rectangles. In addition, we introduce a stochastic local search algorithm performing on potentially optimal hyper-rectangles to improve the solution quality and convergence speed. Global convergence of the StepDIRECT algorithm is provided. Numerical experiments on optimization for random forest models and hyper-parameter tuning are presented to support the efficacy of our algorithm. The proposed StepDIRECT algorithm shows competitive performance results compared with other state-of-the-art baseline DFO methods including the original DIRECT algorithm.
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