# Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming

arXiv: https://arxiv.org/abs/1904.01934 · HTML: https://mlsanity.com/paper/1904.01934/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

## Built on by (most cited first, 14 of 14)

- [Look Before You Leap: An Exploratory Study of Uncertainty Measurement for Large Language Models](https://mlsanity.com/paper/2307.10236/) (2023)
- [Maximizing information from chemical engineering data sets: Applications to machine learning](https://mlsanity.com/paper/2201.10035/) (2022)
- [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024)
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- [MPAX: Mathematical Programming in JAX](https://mlsanity.com/paper/2412.09734/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning](https://mlsanity.com/paper/2106.03279/) (2021)
- [Expecting The Unexpected: Towards Broad Out-Of-Distribution Detection](https://mlsanity.com/paper/2308.11480/) (2023)
- [Adaptive Learning for the Resource-Constrained Classification Problem](https://mlsanity.com/paper/2207.09196/) (2022)
- [Reinforcement Learning-Driven Plant-Wide Refinery Planning Using Model Decomposition](https://mlsanity.com/paper/2504.08642/) (2025)
- [Optimality Principles and Neural Ordinary Differential Equations-based Process Modeling for Distributed Control](https://mlsanity.com/paper/2508.04799/) (2025)
- [Revealing Neurocognitive and Behavioral Patterns by Unsupervised Manifold Learning from Dynamic Brain Data](https://mlsanity.com/paper/2508.11672/) (2025)
- [Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs](https://mlsanity.com/paper/2606.21440/) (2026)

## Abstract (arXiv)

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.