Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function

• URL: http://arxiv.org/abs/2112.14949v1
• Date: Thu, 30 Dec 2021 07:19:59 GMT
• Title: Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function
• Authors: Lei Wang, Xin Liu
• Abstract summary: This paper focuses on the decentralized optimization problem over the Stiefel manifold. Agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence. This paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration.
• Score: 7.768673476492471
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we focus on the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of $d$ agents. The objective is an average of $d$ local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems.

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