# Learning optimization models in the presence of unknown relations

arXiv: https://arxiv.org/abs/1401.1061 · HTML: https://mlsanity.com/paper/1401.1061/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2014.

## Built on by (most cited first, 10 of 10)

- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Optimal randomized classification trees](https://mlsanity.com/paper/2110.11952/) (2021)
- [Counterfactual Explanations Using Optimization With Constraint Learning](https://mlsanity.com/paper/2209.10997/) (2022)
- [BAT: Benchmark for Auto-bidding Task](https://mlsanity.com/paper/2505.08485/) (2025)
- [Optimizing over an ensemble of neural networks](https://mlsanity.com/paper/2112.07007/) (2021)
- [Constraint Learning to Define Trust Regions in Predictive-Model Embedded Optimization](https://mlsanity.com/paper/2201.04429/) (2022)
- [SimPO: Simultaneous Prediction and Optimization](https://mlsanity.com/paper/2204.00062/) (2022)
- [Tight Mixed-Integer Optimization Formulations for Prescriptive Trees](https://mlsanity.com/paper/2302.14744/) (2023)
- [Output-Constrained Decision Trees](https://mlsanity.com/paper/2405.15314/) (2024)

## Abstract (arXiv)

In a sequential auction with multiple bidding agents, it is highly challenging to determine the ordering of the items to sell in order to maximize the revenue due to the fact that the autonomy and private information of the agents heavily influence the outcome of the auction. The main contribution of this paper is two-fold. First, we demonstrate how to apply machine learning techniques to solve the optimal ordering problem in sequential auctions. We learn regression models from historical auctions, which are subsequently used to predict the expected value of orderings for new auctions. Given the learned models, we propose two types of optimization methods: a black-box best-first search approach, and a novel white-box approach that maps learned models to integer linear programs (ILP) which can then be solved by any ILP-solver. Although the studied auction design problem is hard, our proposed optimization methods obtain good orderings with high revenues. Our second main contribution is the insight that the internal structure of regression models can be efficiently evaluated inside an ILP solver for optimization purposes. To this end, we provide efficient encodings of regression trees and linear regression models as ILP constraints. This new way of using learned models for optimization is promising. As the experimental results show, it significantly outperforms the black-box best-first search in nearly all settings.