Sparsity-Exploiting Distributed Projections onto a Simplex

TL;DR

This paper introduces a parallel algorithm for projecting vectors onto a simplex, optimized for sparse solutions in large-scale problems, and extends existing serial algorithms with theoretical analysis and practical validation.

Contribution

It presents a novel parallel projection method onto a simplex that is effective for sparse solutions and adaptable to existing serial algorithms, with theoretical and empirical validation.

Findings

Effective in large-scale sparse problems

Parallelization improves computational efficiency

Validated on real-world and simulated data

Abstract

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been on serial algorithms. We present a parallel method that decomposes the input vector and distributes it across multiple processors for local projection. Our method is especially effective when the resulting projection is highly sparse; which is the case, for instance, in large-scale problems with i.i.d. entries. Moreover, the method can be adapted to parallelize a broad range of serial algorithms from the literature. We fill in theoretical gaps in serial algorithm analysis, and develop similar results for our parallel analogues. Numerical experiments conducted on a wide range of large-scale instances, both real-world and simulated, demonstrate the practical effectiveness of the method.