Jinming Xu — Page 3

arXiv2019

A Push-Pull Gradient Method for Distributed Optimization in Networks

In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider a new distributed gradient-based method where each node maintains two estimates, namely, an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents' objective functions. From the viewpoint of an agent, the information about the decision variable is pushed to the neighbors, while the information about the gradients is pulled from the neighbors (hence giving the name "push-pull gradient method"). The method unifies the algorithms with different types of distributed architecture, including decentralized (peer-to-peer), centralized (master-slave), and semi-centralized (leader-follower) architecture. We show that the algorithm converges linearly for strongly convex and smooth objective functions over a directed static network. In our numerical test, the algorithm performs well even for time-varying directed networks.

math.OC↗

arXiv2016

A Bregman Splitting Algorithm for Distributed Optimization over Networks

We consider distributed optimization problems in which a group of agents are to collaboratively seek the global optimum through peer-to-peer communication networks. The problem arises in various application areas, such as resource allocation, sensor fusion and distributed learning. We propose a general efficient distributed algorithm--termed Distributed Forward-Backward Bregman Splitting (D-FBBS)--to simultaneously solve the above primal problem as well as its dual based on Bregman method and operator splitting. The proposed algorithm allows agents to communicate asynchronously and thus lends itself to stochastic networks. This algorithm belongs to the family of general proximal point algorithms and is shown to have close connections with some existing well-known algorithms when dealing with fixed networks. However, we will show that it is generally different from the existing ones due to its effectiveness in handling stochastic networks. With proper assumptions, we establish a non-ergodic convergence rate of o(1/k) in terms of fixed point residuals over fixed networks both for D-FBBS and its inexact version (ID-FBBS) which is more computationally efficient and an ergodic convergence rate of O(1/k) for D-FBBS over stochastic networks respectively. We also apply the proposed algorithm to sensor fusion problems to show its superior performance compared to existing methods.

math.OC↗