Asynchronous Multi-Agent Primal-Dual Optimization

TL;DR

This paper introduces an asynchronous primal-dual optimization framework for multi-agent networks with a centralized cloud, allowing flexible communication timings while ensuring convergence through synchronization of dual variables.

Contribution

It proposes a novel asynchronous primal-dual method with minimal coordination, incorporating Tikhonov regularization and demonstrating convergence guarantees.

Findings

Convergence is achieved under mild asynchronous communication conditions.

Synchronization of dual variables across agents is necessary for convergence.

Simulation results confirm the effectiveness of the proposed algorithm.

Abstract

We present a framework for asynchronously solving convex optimization problems over networks of agents which are augmented by the presence of a centralized cloud computer. This framework uses a Tikhonov-regularized primal-dual approach in which the agents update the system's primal variables and the cloud updates its dual variables. To minimize coordination requirements placed upon the system, the times of communications and computations among the agents are allowed to be arbitrary, provided they satisfy mild conditions. Communications from the agents to the cloud are likewise carried out without any coordination in their timing. However, we require that the cloud keep the dual variable's value synchronized across the agents, and a counterexample is provided that demonstrates that this level of synchrony is indeed necessary for convergence. Convergence rate estimates are provided in both the primal and dual spaces, and simulation results are presented that demonstrate the operation and convergence of the proposed algorithm.