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Cooperative Data-Driven Distributionally Robust Optimization
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DOI：10.1109/TAC.2019.2955031.png)
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Abstract
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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.
Keywords:
Optimization
Random variables
Probability distribution
Measurement
Distributed algorithms
Linear programming
Convex functions
Data-driven methods
distributed optimization
distributionally robust optimization
multiagent systems
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