An Approximate, Efficient Solver for LP Rounding

TL;DR

This paper introduces an efficient approximate LP solver that uses stochastic coordinate descent, enabling faster solutions for combinatorial problems with comparable quality to exact LP solvers.

Contribution

It presents a novel approximate LP solving method using stochastic coordinate descent with theoretical guarantees and practical efficiency improvements.

Findings

Up to ten times faster than Cplex on benchmark problems

Achieves solution quality comparable to exact LP solvers

Provides theoretical bounds on runtime and solution accuracy

Abstract

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex- act one. These approximate LP solutions can be computed efficiently by applying a parallel stochastic-coordinate-descent method to a quadratic-penalty formulation of the LP. We derive worst-case runtime and solution quality guarantees of this scheme using novel perturbation and convergence analysis. Our experiments demonstrate that on such combinatorial problems as vertex cover, independent set and multiway-cut, our approximate rounding scheme is up to an order of magnitude faster than Cplex (a commercial LP solver) while producing solutions of similar quality.