PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming

TL;DR

This paper introduces PDHG-Net, a neural network unrolled from the PDHG method, combined with a two-stage approach to significantly accelerate large-scale linear programming solutions.

Contribution

It proposes a novel neural network architecture unrolled from PDHG and a two-stage inference method for faster LP solving, with theoretical recovery guarantees.

Findings

Achieves up to 3x speedup over first-order methods.

Can approximate LP solutions with a polynomial number of neurons.

Combines neural network and traditional algorithms for improved efficiency.

Abstract

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3$\times$ speedup compared to FOMs for large-scale LP problems.