# From Predictive to Prescriptive Analytics

arXiv: https://arxiv.org/abs/1402.5481 · HTML: https://mlsanity.com/paper/1402.5481/

## Key facts

- Cited by 143 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2014.

## Built on by (most cited first, 30 of 143)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
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- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Learning from a Biased Sample](https://mlsanity.com/paper/2209.01754/) (2022)
- [Decision-Aware Learning for Optimizing Health Supply Chains](https://mlsanity.com/paper/2211.08507/) (2022)
- [Contextual Stochastic Bilevel Optimization](https://mlsanity.com/paper/2310.18535/) (2023)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Online Contextual Decision-Making with a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2206.07316/) (2022)
- [On the Fairness of Machine-Assisted Human Decisions](https://mlsanity.com/paper/2110.15310/) (2021)
- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective](https://mlsanity.com/paper/2304.06412/) (2023)
- [What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimization](https://mlsanity.com/paper/2505.21692/) (2025)
- [A Framework for Inherently Interpretable Optimization Models](https://mlsanity.com/paper/2208.12570/) (2022)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [Learning to optimize: A tutorial for continuous and mixed-integer optimization](https://mlsanity.com/paper/2405.15251/) (2024)
- [Allocation Requires Prediction Only if Inequality Is Low](https://mlsanity.com/paper/2406.13882/) (2024)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [On the Reliability Limits of LLM-Based Multi-Agent Planning](https://mlsanity.com/paper/2603.26993/) (2026)
- [Explainable Data-Driven Optimization: From Context to Decision and Back Again](https://mlsanity.com/paper/2301.10074/) (2023)

## Abstract (arXiv)

In this paper, we combine ideas from machine learning (ML) and operations research and management science (OR/MS) in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications of OR/MS, we consider data consisting, not only of observations of quantities with direct effect on costs/revenues, such as demand or returns, but predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate that our proposed solution methods, which are inspired by ML methods such as local regression, CART, and random forests, are generally applicable to a wide range of decision problems. We prove that they are tractable and asymptotically optimal even when data is not iid and may be censored. We extend this to the case where decision variables may directly affect uncertainty in unknown ways, such as pricing's effect on demand. As an analogue to R2, we develop a metric P termed the coefficient of prescriptiveness to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1bil units per year. We leverage internal data and public online data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, accounts for an 88% improvement as measured by our P.