Cooperative Data-Driven Distributionally Robust Optimization
Cooperative Data-Driven Distributionally Robust Optimization
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DOI：
10.1109/tac.2019.2955031
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发表时间：
2020-10-01
影响因子：
6.8
通讯作者：
Cortes, Jorge
中科院分区：
文献类型：
--
作者：
Cherukuri, Ashish;Cortes, Jorge
我们研究了一类多智能体随机优化问题，其目标是最小化依赖于随机变量的函数的期望值。随机变量的概率分布对于智能体是未知的。智能体的目标是利用它们收集到的数据，合作寻找一个保证样本外性能的解决方案。该方法是使用Wasserstein模糊集来制定一个数据驱动的分布鲁棒优化问题，这相当于一个凸规划。我们将后者重新表述为一个分布式优化问题，并确定了一个凸凹增广拉格朗日，其鞍点对应于优化器，前提是满足最小-最大互换性准则。然后，我们的分布式算法设计由与增广拉格朗日量相关的鞍点动力学组成。我们正式地建立了轨迹渐近地收敛于鞍点，因此是问题的优化器。最后，我们确定了满足最小-最大互换性准则的函数类。
We study a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown to the agents. The agents aim to cooperatively find, using their collected data, a solution with guaranteed out-of-sample performance. The approach is to formulate a data-driven distributionally robust optimization problem using Wasserstein ambiguity sets, which turns out to be equivalent to a convex program. We reformulate the latter as a distributed optimization problem and identify a convex-concave augmented Lagrangian, whose saddle points are in correspondence with the optimizers, provided a min-max interchangeability criteria is met. Our distributed algorithm design, then consists of the saddle-point dynamics associated to the augmented Lagrangian. We formally establish that the trajectories converge asymptotically to a saddle point and, hence, an optimizer of the problem. Finally, we identify classes of functions that meet the min-max interchangeability criteria.