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This work studies multi-agent sharing optimization problems with theobjective function being the sum of smooth local functions plus a convex(possibly non-smooth) function coupling all agents. This scenario arises inmany machine learning and engineering applications, such as regression overdistributed features and resource allocation. We reformulate this problem intoan equivalent saddle-point problem, which is amenable to decentralizedsolutions. We then propose a proximal primal-dual algorithm and establish itslinear convergence to the optimal solution when the local functions arestrongly-convex. To our knowledge, this is the first linearly convergentdecentralized algorithm for multi-agent sharing problems with a general convex(possibly non-smooth) coupling function.

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features