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

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.

23 pages, 5 figures

References in corpus (6)

• A Linearly Convergent Algorithm for Distributed Principal Component Analysis
• FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis
• DeEPCA: Decentralized Exact PCA with Linear Convergence Rate
• A Communication-Efficient and Privacy-Aware Distributed Algorithm for Sparse PCA
• A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold
• Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function

Cited by in corpus (2)

• A Communication-Efficient and Privacy-Aware Distributed Algorithm for Sparse PCA
• Seeking Consensus on Subspaces in Federated Principal Component Analysis