Sensitivity Assisted Alternating Directions Method of Multipliers for Distributed Optimization and Statistical Learning

TL;DR

This paper introduces a sensitivity-assisted ADMM algorithm that reduces computational complexity in distributed optimization by approximating subproblem solutions with parametric sensitivities, demonstrated on nonlinear estimation and neural network tasks.

Contribution

It proposes a novel sensitivity-assisted ADMM method that leverages parametric sensitivities to approximate solutions, improving efficiency in distributed learning.

Findings

The algorithm converges under certain conditions.

It significantly reduces computational effort in subproblem solving.

Numerical experiments show improved efficiency on real problems.

Abstract

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The different subproblems can be solved in parallel by a set of worker computing nodes coordinated by a master node, and the subproblems are repeatedly solved until convergence. At each iteration, the worker nodes must solve a convex optimization problem whose difficulty increases with the size of the problem. In this paper, we propose a sensitivity-assisted ADMM algorithm that leverages the parametric sensitivities such that the subproblems solutions can be approximated using a tangential predictor, thus easing the computational burden to computing one linear solve. We study the convergence properties of the proposed sensitivity-assisted ADMM algorithm. The numerical performance of the algorithm is illustrated on a nonlinear parameter estimation problem, and a multilayer perceptron learning problem.