论文标题
同时控制参数依赖系统的随机优化方法
Stochastic optimization methods for the simultaneous control of parameter-dependent systems
论文作者
论文摘要
我们解决随机优化方法的应用，以同时控制参数依赖性系统。特别是，我们专注于罗宾斯和梦想的经典随机梯度下降（SGD）方法，以及最近开发的连续随机梯度（CSG）算法。我们考虑通过最小化成本功能定义为每个系统实现的个人成本的叠加来计算同时控制的问题。我们将这些随机方法的性能（从它们的计算复杂性）与更经典的梯度下降（GD）和共轭梯度（CG）算法进行比较，我们讨论了每种方法的优势和缺点。与公认的机器学习环境中的结果一致，我们展示了SGD和CSG算法如何根据大量参数处理控制问题时可以显着减轻计算负担。这是通过数值实验来证实的。
We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the recently developed Continuous Stochastic Gradient (CSG) algorithm. We consider the problem of computing simultaneous controls through the minimization of a cost functional defined as the superposition of individual costs for each realization of the system. We compare the performances of these stochastic approaches, in terms of their computational complexity, with those of the more classical Gradient Descent (GD) and Conjugate Gradient (CG) algorithms, and we discuss the advantages and disadvantages of each methodology. In agreement with well-established results in the machine learning context, we show how the SGD and CSG algorithms can significantly reduce the computational burden when treating control problems depending on a large amount of parameters. This is corroborated by numerical experiments.
