A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming

TL;DR

This paper introduces a hybrid learning-to-optimize framework that accelerates solving parametric MIQP problems by combining neural networks, differentiable QP layers, and hybrid loss functions, specifically targeting MI-MPC applications.

Contribution

It presents a novel hybrid L2O framework integrating supervised and self-supervised learning with differentiable QP layers for improved MIQP solution prediction.

Findings

Demonstrated effectiveness on two benchmark MI-MPC problems

Outperformed purely supervised and self-supervised models

Enhanced optimality and feasibility in predicted solutions

Abstract

In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models.