# JANOS: An Integrated Predictive and Prescriptive Modeling Framework

arXiv: https://arxiv.org/abs/1911.09461 · HTML: https://mlsanity.com/paper/1911.09461/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 27 of 27)

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- [Scaling Up Exact Neural Network Compression by ReLU Stability](https://mlsanity.com/paper/2102.07804/) (2021)
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- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modeling](https://mlsanity.com/paper/2510.27610/) (2025)
- [Modeling Design and Control Problems Involving Neural Network Surrogates](https://mlsanity.com/paper/2111.10489/) (2021)
- [Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions](https://mlsanity.com/paper/2301.07966/) (2023)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks](https://mlsanity.com/paper/2312.16699/) (2023)
- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)
- [Towards Improving Unit Commitment Economics: An Add-On Tailor for Renewable Energy and Reserve Predictions](https://mlsanity.com/paper/2208.13065/) (2022)
- [How to predict and optimise with asymmetric error metrics](https://mlsanity.com/paper/2211.13586/) (2022)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [One-for-many Counterfactual Explanations by Column Generation](https://mlsanity.com/paper/2402.09473/) (2024)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [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)
- [Multi-Objective Linear Ensembles for Robust and Sparse Training of Few-Bit Neural Networks](https://mlsanity.com/paper/2212.03659/) (2022)
- [Tight Mixed-Integer Optimization Formulations for Prescriptive Trees](https://mlsanity.com/paper/2302.14744/) (2023)
- [Learning Decisions Offline from Censored Observations with ε-insensitive Operational Costs](https://mlsanity.com/paper/2408.07305/) (2024)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [Optimization with Dynamic Constraint Learning (DCL)](https://mlsanity.com/paper/2607.25719/) (2026)
- [Representation Learning for Exact Preimages](https://mlsanity.com/paper/2609.32018/) (2026)

## Abstract (arXiv)

Business research practice is witnessing a surge in the integration of predictive modeling and prescriptive analysis. We describe a modeling framework JANOS that seamlessly integrates the two streams of analytics, for the first time allowing researchers and practitioners to embed machine learning models in an optimization framework. JANOS allows for specifying a prescriptive model using standard optimization modeling elements such as constraints and variables. The key novelty lies in providing modeling constructs that allow for the specification of commonly used predictive models and their features as constraints and variables in the optimization model. The framework considers two sets of decision variables; regular and predicted. The relationship between the regular and the predicted variables are specified by the user as pre-trained predictive models. JANOS currently supports linear regression, logistic regression, and neural network with rectified linear activation functions, but we plan to expand on this set in the future. In this paper, we demonstrate the flexibility of the framework through an example on scholarship allocation in a student enrollment problem and provide a numeric performance evaluation.