论文标题
通过分布式的半无限编程，通过网络对数据驱动的分配优化在网络上进行了强大的优化
Data-driven distributionally robust optimization over a network via distributed semi-infinite programming
论文作者
论文摘要
本文着重于在代理网络上解决数据驱动的分布强劲优化问题。这些代理商的目的是最大程度地减少以经验分布为中心的Wasserstein模棱两可的含糊不清集合所计算出的最糟糕的预期成本。不确定性样本分布在整个代理商中。我们的方法包括将问题重新解决为半无限程序，然后设计分布式算法，该算法解决了一个通用的半无限问题，该问题具有与重新计算问题相同的信息结构。特别是，决策变量由代理可以自由优化的本地元素和需要达成共识的全球性变量组成。我们的分布式算法是一个迭代过程，它结合了分布式ADMM和切割表面方法的概念。我们表明，迭代渐近地收敛到分布鲁棒问题的解决方案，从而获得了任何预先指定的准确性。模拟说明了我们的结果。
This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the empirical distribution. The samples of the uncertainty are distributed across the agents. Our approach consists of reformulating the problem as a semi-infinite program and then designing a distributed algorithm that solves a generic semi-infinite problem that has the same information structure as the reformulated problem. In particular, the decision variables consist of both local ones that agents are free to optimize over and global ones where they need to agree on. Our distributed algorithm is an iterative procedure that combines the notions of distributed ADMM and the cutting-surface method. We show that the iterates converge asymptotically to a solution of the distributionally robust problem to any pre-specified accuracy. Simulations illustrate our results.
