相关论文: Riemannian EXTRA: Communication-efficient decentra…

Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian…

Gradient descent with momentum has been widely applied in various signal processing and machine learning tasks, demonstrating a notable empirical advantage over standard gradient descent. However, momentum-based distributed Riemannian…

Decentralized optimization provides a fundamental framework for large-scale learning and signal processing with distributed data. We study decentralized optimization with orthogonality constraints on the Stiefel manifold and propose…

We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local…

Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as…

This paper develops a fast distributed algorithm, termed \emph{DEXTRA}, to solve the optimization problem when~$n$ agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the…

We consider the problem of decentralized nonconvex optimization over a compact submanifold, where each local agent's objective function defined by the local dataset is smooth. Leveraging the powerful tool of proximal smoothness, we…

This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…

This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly…

We are concerned with decentralized optimization over a compact submanifold, where the loss functions of local datasets are defined by their respective local datasets. A key challenge in decentralized optimization is mitigating the…

We consider the consensus problem in a decentralized network, focusing on a compact submanifold that acts as a nonconvex constraint set. By leveraging the proximal smoothness of the compact submanifold, which encompasses the local singleton…

This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

This paper studies decentralized optimization over a compact submanifold within a communication network of $n$ nodes, where each node possesses a smooth non-convex local cost function, and the goal is to jointly minimize the sum of these…

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel…

Recently, there have been growing interests in solving consensus optimization problems in a multi-agent network. In this paper, we develop a decentralized algorithm for the consensus optimization problem…