Asynchronous Optimization Over Heterogeneous Networks via Consensus ADMM

TL;DR

This paper introduces asynchronous distributed ADMM algorithms for non-convex optimization over heterogeneous networks, enabling nodes to skip updates and still guarantee convergence to local minima, with applications in wireless localization.

Contribution

It proposes novel asynchronous ADMM variants that handle non-convex functions and partial updates, improving robustness and efficiency in distributed optimization.

Findings

Algorithms converge to local minima under regularity conditions.

Proposed methods outperform existing localization algorithms.

Applicable to multi-agent systems with heterogeneous data.

Abstract

This paper considers the distributed optimization of a sum of locally observable, non-convex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An asynchronous and distributed alternating directions method of multipliers (ADMM) method that allows the nodes to defer or skip the computation and transmission of updates is proposed in the paper. The proposed algorithm utilizes different approximations in the update step, resulting in proximal and majorized ADMM variants. Both variants are shown to converge to a local minimum, under certain regularity conditions. The proposed asynchronous algorithms are also applied to the problem of cooperative localization in wireless ad hoc networks, where it is shown to outperform the other state-of-the-art localization algorithms.