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Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems

Mustafa O. KarabagDavid Fridovich-KeilUfuk Topcu
Sep 2022
摘要
Saddle-point problems appear in various settings including machine learning,zero-sum stochastic games, and regression problems. We consider decomposablesaddle-point problems and study an extension of the alternating directionmethod of multipliers to such saddle-point problems. Instead of solving theoriginal saddle-point problem directly, this algorithm solves smallersaddle-point problems by exploiting the decomposable structure. We show theconvergence of this algorithm for convex-concave saddle-point problems under amild assumption. We also provide a sufficient condition for which theassumption holds. We demonstrate the convergence properties of the saddle-pointalternating direction method of multipliers with numerical examples on a powerallocation problem in communication channels and a network routing problem withadversarial costs.
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