Learning to Generate Projections for Reducing Dimensionality of Heterogeneous Linear Programming Problems

Tomoharu Iwata, Shinsaku Sakaue

Abstract: We propose a data-driven method for reducing the dimensionality of linear programming problems (LPs) by generating instance-specific projection matrices using a neural network-based model. Once the model is trained using multiple LPs by maximizing the expected objective value, we can efficiently find high-quality feasible solutions of newly given LPs. Our method can shorten the computational time of any LP solvers due to its solver-agnostic nature, it can provide feasible solutions by relying on projection that reduces the number of variables, and it can handle LPs of different sizes using neural networks with permutation equivariance and invariance. We also provide a theoretical analysis of the generalization bound for learning a neural network to generate projection matrices that reduce the size of LPs. Our experimental results demonstrate that our method can obtain solutions with higher quality than the existing methods, while its computational time is significantly shorter than solving the original LPs.

Lay Summary: We propose a method for more efficiently solving a class of optimization problems, specifically linear programming problems. Our approach uses a neural network to learn how to simplify these problems. Once trained, the model can quickly give good solutions to new problems without solving them from scratch.

Primary Area: Optimization

Keywords: Linear programming, Neural networks, Data-driven algorithm design

Submission Number: 4290