A new bound on the generalization rate of sampled convex programs
A new bound on the generalization rate of sampled convex programs
复制标题
采样凸规划泛化率的新界限
DOI：
10.1109/cdc.2004.1429655
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
M. Campi
中科院分区：
文献类型：
--
作者：
G. Calafiore;M. Campi
本文讨论了鲁棒凸规划的抽样场景方法。它已被证明在以前的作品中，通过随机抽样足够数量的约束之间的（可能的）无限约束的鲁棒凸规划，得到一个标准的凸优化问题，其解决方案是“近似可行的”，在概率意义上，为原来的鲁棒凸规划。这是学习理论意义上的泛化属性，因为满足一定数量的“训练”约束需要满足其他“看不见的”约束。在本文中，我们提供了一个新的有效界的推广速度的采样凸规划，并显示了一个例子的应用程序的鲁棒控制设计问题。
This paper deals with the sampled scenarios approach to robust convex programming. It has been shown in previous works that by randomly sampling a sufficient number of constraints among the (possibly) infinite constraints of a robust convex program, one obtains a standard convex optimization problem whose solution is 'approximately feasible', in a probabilistic sense, for the original robust convex program. This is a generalization property in the learning theoretic sense, since the satisfaction of a certain number of 'training' constraints entails the satisfaction of other 'unseen' constraints. In this paper we provide a new efficient bound on the generalization rate of sampled convex programs, and show an example of application to a robust control design problem.