Conformal Prediction for Early Stopping in Mixed Integer Optimization

TL;DR

This paper introduces a neural network-based conformal prediction method to determine early stopping points in mixed-integer optimization, significantly reducing solve times while maintaining solution quality guarantees.

Contribution

It presents a novel approach combining neural networks and conformal prediction to effectively predict optimality gaps and decide when to stop solvers early.

Findings

Over 60% reduction in solve time on benchmark problems

Guarantees 0.1% optimality with 95% probability

Applicable across multiple problem families from MIPLIB

Abstract

Mixed-integer optimization solvers often find optimal solutions early in the search, yet spend the majority of computation time proving optimality. We exploit this by learning when to terminate solvers early on distributions of similar problem instances. Our method trains a neural network to estimate the true optimality gap from the solver state, then uses conformal prediction to calibrate a stopping threshold with rigorous probabilistic guarantees on solution quality. On five problem families from the distributional MIPLIB library, our method reduces solve time by over 60% while guaranteeing 0.1%- optimal solutions with 95% probability