Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes

Abstract

We consider distributed optimization problems in which a number of agents are to seek the optimum of a global objective function through merely local information sharing. The problem arises in various application domains, such as resource allocation, sensor fusion and distributed learning. In particular, we are interested in scenarios where agents use uncoordinated (different) constant stepsizes for local optimization. According to most existing works, using this kind of stepsize rule for update, which is necessary in asynchronous scenarios, will lead to some gap (error) between the estimated result and the exact optimum. To deal with this issue, we develop a new augmented distributed gradient method (termed Aug-DGM) based on consensus theory. The proposed algorithm not only allows for using uncoordinated stepsizes but also, most importantly, be able to seek the exact optimum even with constant stepsizes assuming that the global objective function has Lipschitz gradient. A simple numerical example is provided to illustrate the effectiveness of the algorithm.

Distributed stochastic optimization with gradient tracking over strongly-connected networks

“…Recently, gradient tracking has been proposed where the local gradient at each agent is replaced by the estimate of the global gradient [12]- [15]. Methods for directed graphs that are based on gradient tracking [14]- [21] rely on separate iterations for eigenvector estimation that may impede the convergence.…”

Distributed Nesterov Gradient Methods Over Arbitrary Graphs

“…Distributed Optimization: The AB algorithm When the objective functions are not available at a central location, distributed solutions are required to solve Problem P1. Most existing work [1]- [3], [11]- [14], [18]- [20] is restricted to undirected graphs, since the weights assigned to neighboring agents must be doubly-stochastic. The work on directed graphs [21], [22], [25]- [28] is largely based on pushsum consensus [29], [30] that requires eigenvector learning.…”

“…It is shown in [33] that AB converges linearly to the optimal solution for the function class F 1,1 µ,L . The AB algorithm for undirected graphs where both weights are doubly-stochastic was studied earlier in [18], [19], [26]. It is shown in [19] that the oracle complexity with doublystochastic weights is O(Q 2 log 1 ).…”

Distributed Optimization for Smart Cyber-Physical Networks

“…More recently, the idea of gradient tracking has been independently proposed by several research groups. In [18,19] the authors consider constrained nonsmooth and nonconvex problems, while in [20,21] strongly convex, unconstrained, smooth optimization problems are addressed. Works [22,23] extend the algorithms to (possibly) time-varying digraphs (still in a nonconvex setting).…”