A Penalty Alternating Direction Method Of Multipliers For Decentralized Composite Optimization
2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING(2020)
摘要
This paper proposes a penalty alternating direction method of multipliers (ADMM) to minimize the summation of convex composite functions over a decentralized network. Each agent in the network holds a private function consisting of a smooth part and a nonsmooth part, and can only exchange information with its neighbors during the optimization process. We consider a penalized approximation of the decentralized optimization problem; but unlike the existing penalty methods, here the penalty parameter can be very small such that the approximation error is negligible. On the other hand, the small penalty parameter makes the penalized objective ill-conditioned, such that the popular proximal gradient descent method has to use a small step size, and is hence slow. To address this issue, we propose to solve the penalized formulation with ADMM. We further utilize the composite structures of the private functions …
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关键词
decentralized optimization, alternating direction method of multipliers (ADMM), composite optimization
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