Distributed Optimization via Adaptive Regularization for Large Problems with Separable Constraints

TL;DR

This paper introduces a parallel distributed optimization algorithm with adaptive regularization, effectively solving large-scale problems with separable constraints faster than existing methods.

Contribution

It proposes a novel adaptive regularizer-based distributed algorithm with proven convergence for large, high-dimensional optimization problems.

Findings

Converges to the optimal solution

Reduces computational time significantly

Performs comparably to existing methods

Abstract

Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm that uses an adaptive regularizer (PDAR) to solve a joint optimization problem with separable constraints. The regularizer is adaptive and depends on the step size between iterations and the iteration number. We show theoretical converge of our algorithm to an optimal solution, and use a multi-agent three-bin resource allocation example to illustrate the effectiveness of the proposed algorithm. Numerical simulations show that our algorithm converges to the same optimal solution as other distributed methods, with significantly reduced computational time.