Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

09/22/2019
by   Vivek Khatana, et al.
0

In this article, a distributed optimization problem for minimizing a sum, ∑_i=1^n f_i, of convex objective functions, f_i, is addressed. Here each function f_i is a function of n variables, private to agent i which defines the agent's objective. Agents can only communicate locally with neighbors defined by a communication network topology. These f_i's are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant which can be determined independently of the network size or topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within O(ρ) where ρ can be chosen to be arbitrarily small.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/08/2019

Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error

Alternating Direction Method of Multipliers (ADMM) is a popular convex o...
research
09/21/2023

Distributed Conjugate Gradient Method via Conjugate Direction Tracking

We present a distributed conjugate gradient method for distributed optim...
research
03/26/2018

DJAM: distributed Jacobi asynchronous method for learning personal models

Processing data collected by a network of agents often boils down to sol...
research
08/01/2017

Distributed multi-agent Gaussian regression via Karhunen-Loève expansions

We consider the problem of distributedly estimating Gaussian random fiel...
research
03/19/2017

A Passivity-Based Distributed Reference Governor for Constrained Robotic Networks

This paper focuses on a passivity-based distributed reference governor (...
research
05/30/2018

On Consensus-Optimality Trade-offs in Collaborative Deep Learning

In distributed machine learning, where agents collaboratively learn from...
research
03/04/2022

Triggered Gradient Tracking for Asynchronous Distributed Optimization

This paper proposes Asynchronous Triggered Gradient Tracking, i.e., a di...

Please sign up or login with your details

Forgot password? Click here to reset