We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the global min--max saddle point. Based on the convergence analysis, we develop a heuristic approach to adapt the learning rate. An implementation of the developed approach using the (1+1)-CMA-ES as the minimization oracle, namely Adversarial-CMA-ES, is shown to outperform several existing approaches on test problems. Numerical evaluation confirms the tightness of the theoretical convergence rate bound as well as the efficiency of the learning rate adaptation mechanism. As an example of real-world problems, the suggested optimization method is applied to automatic berthing control problems under model uncertainties, showing its usefulness in obtaining solutions robust to uncertainty.
翻译:我们建议只依靠能解决尽量减少问题的神器来使点优化上马力的方法。我们分析其趋同特性,分析其强烈的精细结结裂问题,并显示其直线趋同到全球最小和最大马鞍点。根据趋同分析,我们制定了调整学习率的繁忙方法。采用(1+1)-(CMA-ES)的发达方法,作为最小化的神器,即Aversarial-CMA-ES,显示它优于关于测试问题的若干现有方法。数字评价证实了理论趋同率约束的紧凑性以及学习率适应机制的效率。作为现实世界问题的一个例子,所建议的优化方法被用来在模型不确定性下自动处理控制问题,表明它对于获得稳健的不确定性解决办法是有用的。