Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

TL;DR

AUQ-ADMM introduces an adaptive uncertainty-weighted consensus scheme for distributed convex optimization, improving convergence and efficiency especially with many subproblems, demonstrated on machine learning tasks.

Contribution

It proposes a novel adaptive weighting scheme based on solution uncertainty, enhancing distributed ADMM performance with theoretical convergence guarantees.

Findings

Empirically increases progress in consensus ADMM.

Effective in large-scale machine learning applications.

Provides an efficient implementation using PyTorch.

Abstract

We present AUQ-ADMM, an adaptive uncertainty-weighted consensus ADMM method for solving large-scale convex optimization problems in a distributed manner. Our key contribution is a novel adaptive weighting scheme that empirically increases the progress made by consensus ADMM scheme and is attractive when using a large number of subproblems. The weights are related to the uncertainty associated with the solutions of each subproblem, and are efficiently computed using low-rank approximations. We show AUQ-ADMM provably converges and demonstrate its effectiveness on a series of machine learning applications, including elastic net regression, multinomial logistic regression, and support vector machines. We provide an implementation based on the PyTorch package.