# Risk Guarantees for End-to-End Prediction and Optimization Processes

arXiv: https://arxiv.org/abs/2012.15046 · HTML: https://mlsanity.com/paper/2012.15046/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2020.

## Built on by (most cited first, 20 of 20)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (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)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Online Contextual Decision-Making with a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2206.07316/) (2022)
- [Dissecting the Impact of Model Misspecification in Data-driven Optimization](https://mlsanity.com/paper/2503.00626/) (2025)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspective](https://mlsanity.com/paper/2510.18215/) (2025)
- [Decision-Focused Sequential Experimental Design: A Directional Uncertainty-Guided Approach](https://mlsanity.com/paper/2602.05340/) (2026)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints](https://mlsanity.com/paper/2604.20031/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [Learning Decisions Offline from Censored Observations with ε-insensitive Operational Costs](https://mlsanity.com/paper/2408.07305/) (2024)
- ["Over-optimizing" for Normality: Budget-constrained Uncertainty Quantification for Contextual Decision-making](https://mlsanity.com/paper/2503.12747/) (2025)
- [Toward Decision-Oriented Prognostics: An Integrated Estimate-Optimize Framework for Predictive Maintenance](https://mlsanity.com/paper/2506.19698/) (2025)
- [Generating Input Distributions for Explaining Portfolio Optimization Pipelines](https://mlsanity.com/paper/2606.25808/) (2026)
- [Smart predict-then-robustly-optimize](https://mlsanity.com/paper/2607.21773/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)
- [Geometric Identification in Predict-Then-Optimize Learning](https://mlsanity.com/paper/2609.33472/) (2026)

## Abstract (arXiv)

Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own. While it is usually believed that good prediction performance in estimating the parameters will result in good subsequent optimization performance, formal theoretical guarantees on this are notably lacking. In this paper, we explore conditions that allow us to explicitly describe how the prediction performance governs the optimization performance. Our weaker condition allows for an asymptotic convergence result, while our stronger condition allows for exact quantification of the optimization performance in terms of the prediction performance. In general, verification of these conditions is a non-trivial task. Nevertheless, we show that our weaker condition is equivalent to the well-known Fisher consistency concept from the learning theory literature. This then allows us to easily check our weaker condition for several loss functions. We also establish that the squared error loss function satisfies our stronger condition. Consequently, we derive the exact theoretical relationship between prediction performance measured with the squared loss, as well as a class of symmetric loss functions, and the subsequent optimization performance. In a computational study on portfolio optimization, fractional knapsack and multiclass classification problems, we compare the optimization performance of using of several prediction loss functions (some that are Fisher consistent and some that are not) and demonstrate that lack of consistency of the loss function can indeed have a detrimental effect on performance.