# Learning for Online Mixed-Integer Model Predictive Control with Parametric Optimality Certificates

arXiv: https://arxiv.org/abs/2303.12152 · HTML: https://mlsanity.com/paper/2303.12152/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2023.

## Built on by (most cited first, 2 of 2)

- [Integrating Reinforcement Learning and Model Predictive Control with Applications to Microgrids](https://mlsanity.com/paper/2409.11267/) (2024)
- [ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs](https://mlsanity.com/paper/2512.10211/) (2025)

## Abstract (arXiv)

We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions. Inspired by Branch-and-Bound techniques, the key idea is to train a Neural Network/Random Forest, which for a given parameter, predicts a strategy consisting of (1) a set of Linear Programs (LPs) such that their feasible sets form a partition of the feasible set of the MILP and (2) a candidate integer solution. For control computation and sub-optimality quantification, we solve a set of LPs online in parallel. We demonstrate our approach for a motion planning example and compare against various commercial and open-source mixed-integer programming solvers.