# Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design

arXiv: https://arxiv.org/abs/2209.09404 · HTML: https://mlsanity.com/paper/2209.09404/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 9 of 9)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [Ambulance Emergency Response Optimization in Developing Countries](https://mlsanity.com/paper/1801.05402/) (2018)
- [Problem-Driven Scenario Clustering in Stochastic Optimization](https://mlsanity.com/paper/2106.11717/) (2021)
- [Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs. Extended version and complete risk profiles analysis](https://mlsanity.com/paper/1804.04174/) (2018)
- [When Nash Meets Stackelberg](https://mlsanity.com/paper/1910.06452/) (2019)
- [Urban Bike Lane Planning with Bike Trajectories: Models, Algorithms, and a Real-World Case Study](https://mlsanity.com/paper/2008.09645/) (2020)

## Built on by (most cited first, 3 of 3)

- [AutoLTS: Automating Cycling Stress Assessment via Contrastive Learning and Spatial Post-processing](https://mlsanity.com/paper/2308.07580/) (2023)
- [Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application](https://mlsanity.com/paper/2606.25362/) (2026)
- [Learning-Augmented Optimization for Strategic Two-Echelon Spare Parts Network Design](https://mlsanity.com/paper/2609.12524/) (2026)

## Abstract (arXiv)

A wide range of decision problems can be formulated as bilevel programs with independent followers, which as a special case include two-stage stochastic programs. These problems are notoriously difficult to solve especially when a large number of followers present. Motivated by a real-world cycling infrastructure planning application, we present a general approach to solving such problems. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. We prove bounds on the optimality gap of the generated leader decision as measured by the original objective function that considers the full follower set. We then develop follower sampling algorithms to tighten the bounds and a representation learning approach to learn follower features, which are used as inputs to the embedded machine learning model. Through numerical studies, we show that our approach generates leader decisions of higher quality compared to baselines. Finally, in collaboration with the City of Toronto, we perform a real-world case study in Toronto where we solve a cycling network design problem with over one million followers. Compared to the current practice, our approach improves Toronto's cycling accessibility by 19.2%, equivalent to 18M in potential cost savings. Our approach is being used to inform the cycling infrastructure planning in Toronto and outperforms the current practice by a large margin. It can be generalized to any decision problems that are formulated as bilevel programs with independent followers.