# Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective

arXiv: https://arxiv.org/abs/2304.06833 · HTML: https://mlsanity.com/paper/2304.06833/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 84 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 30 of 35)

- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Generalization Bounds in the Predict-then-Optimize Framework](https://mlsanity.com/paper/1905.11488/) (2019)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)
- [Asymptotic Optimality in Stochastic Optimization](https://mlsanity.com/paper/1612.05612/) (2016)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (2021)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Stochastic Optimization Forests](https://mlsanity.com/paper/2008.07473/) (2020)
- [Risk Guarantees for End-to-End Prediction and Optimization Processes](https://mlsanity.com/paper/2012.15046/) (2020)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)
- [Data-Pooling in Stochastic Optimization](https://mlsanity.com/paper/1906.00255/) (2019)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Decision-Aware Learning for Optimizing Health Supply Chains](https://mlsanity.com/paper/2211.08507/) (2022)
- [A bilevel framework for decision-making under uncertainty with contextual information](https://mlsanity.com/paper/2008.01500/) (2020)
- [On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach](https://mlsanity.com/paper/2110.04855/) (2021)
- [How Big Should Your Data Really Be? Data-Driven Newsvendor: Learning One Sample at a Time](https://mlsanity.com/paper/2107.02742/) (2021)
- [Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2107.12438/) (2021)

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

- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [A Comprehensive Review of AI Agents: Transforming Possibilities in Technology and Beyond](https://mlsanity.com/paper/2508.11957/) (2025)
- [The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspective](https://mlsanity.com/paper/2510.18215/) (2025)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [What is the Right Notion of Distance between Predict-then-Optimize Tasks?](https://mlsanity.com/paper/2409.06997/) (2024)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2602.03690/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [End-to-End Fairness Optimization with Fair Decision-Focused Learning](https://mlsanity.com/paper/2607.29441/) (2026)
- [Exploring End-to-end Differentiable Neural Charged Particle Tracking -- A Loss Landscape Perspective](https://mlsanity.com/paper/2407.13420/) (2024)
- [Toward Decision-Oriented Prognostics: An Integrated Estimate-Optimize Framework for Predictive Maintenance](https://mlsanity.com/paper/2506.19698/) (2025)
- [Simulating Classification Models for Ex-Ante Evaluation of Predict-Then-Optimize Methods](https://mlsanity.com/paper/2509.02191/) (2025)
- [Scalable Decision Focused Learning via Online Trainable Surrogates](https://mlsanity.com/paper/2512.03861/) (2025)
- [Integrated Prediction and Multi-period Portfolio Optimization](https://mlsanity.com/paper/2512.11273/) (2025)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition](https://mlsanity.com/paper/2606.08797/) (2026)
- [Weak-to-Strong Learning in Decision Making](https://mlsanity.com/paper/2607.18467/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)

## Abstract (arXiv)

In data-driven stochastic optimization, model parameters of the underlying distribution need to be estimated from data in addition to the optimization task. Recent literature considers integrating the estimation and optimization processes by selecting model parameters that lead to the best empirical objective performance. This integrated approach, which we call integrated-estimation-optimization (IEO), can be readily shown to outperform simple estimate-then-optimize (ETO) when the model is misspecified. In this paper, we show that a reverse behavior appears when the model class is well-specified and there is sufficient data. Specifically, for a general class of nonlinear stochastic optimization problems, we show that simple ETO outperforms IEO asymptotically when the model class covers the ground truth, in the strong sense of stochastic dominance of the regret. Namely, the entire distribution of the regret, not only its mean or other moments, is always better for ETO compared to IEO. Our results also apply to constrained, contextual optimization problems where the decision depends on observed features. Whenever applicable, we also demonstrate how standard sample average approximation (SAA) performs the worst when the model class is well-specified in terms of regret, and best when it is misspecified. Finally, we provide experimental results to support our theoretical comparisons and illustrate when our insights hold in finite-sample regimes and under various degrees of misspecification.