Dissecting the Impact of Model Misspecification in Data-driven Optimization

Adam N. Elmachtoub; Henry Lam; Haixiang Lan; Haofeng Zhang

cs.LGMar 1, 2025

Dissecting the Impact of Model Misspecification in Data-driven Optimization

Authors: Adam N. Elmachtoub, Henry Lam, Haixiang Lan, Haofeng Zhang

Organizations: Columbia University · Morgan Stanley

Abstract

Data-driven optimization aims to translate a machine learning model into decision-making by optimizing decisions on estimated costs. Such a pipeline can be conducted by fitting a distributional model which is then plugged into the target optimization problem. While this fitting can utilize traditional methods such as maximum likelihood, a more recent approach uses estimation-optimization integration that minimizes decision error instead of estimation error. Although intuitive, the statistical benefit of the latter approach is not well understood yet is important to guide the prescriptive usage of machine learning. In this paper, we dissect the performance comparisons between these approaches in terms of the amount of model misspecification. In particular, we show how the integrated approach offers a ``universal double benefit'' on the top two dominating terms of regret when the underlying model is misspecified, while the traditional approach can be advantageous when the model is nearly well-specified. Our comparison is powered by finite-sample tail regret bounds that are derived via new higher-order expansions of regrets and the leveraging of a recent Berry-Esseen theorem.

Figures & tables

Model Misspecification	$\kappa_{0}^{\textup{IEO}}<t<\kappa_{0}^{\textup{ETO}}$	$t>\kappa_{0}^{\textup{ETO}}$
$\delta\gg 0$	$\mathcal{D}\geq 1-\epsilon_{n,t}$	$\mathcal{D}\geq-\epsilon_{n,t}$
$\delta>0$ , $\tau_{1}>0$ , $H^{\textup{ETO}}>0$	$\mathcal{D}\geq 1-\epsilon_{n,t}$	$\mathcal{D}\leq\epsilon_{n,t}$ (for only large $t$ )
$\delta=0$ , $C_{\textup{mis}}B_{0}\leq\tau_{3}$ , $H^{\textup{ETO}}>0$	N/A (since $\kappa_{0}^{\textup{IEO}}=\kappa_{0}^{\textup{ETO}}$ )	$\mathcal{D}\leq\epsilon_{n,t}$
$\delta=0$ and $B_{0}=0$	N/A (since $\kappa_{0}^{\textup{IEO}}=\kappa_{0}^{\textup{ETO}}$ )	$\mathcal{D}\leq-C_{n,t}+\epsilon_{n,t}$

Table 1: Summary of the comparisons between ETO and IEO. The results are expressed in terms of the tail probability difference

\mathcal{D}=\mathbb{P}(R(\hat{{\bm{w}}}^{{\textup{ETO}}})\geq t)-\mathbb{P}(R(\hat{{\bm{w}}}^{{\textup{IEO}}})\geq t)

\epsilon_{n,t}

is a small constant vanishing as the sample size

n

increases.

Model Misspecification

Model misspecification studies how predictions and decisions fail when a model’s assumptions or structure do not match the data-generating process.

See all 29 papers

Decision-Driven Regularization: A Blended Model for Learning and Optimization
Aug 15, 2026Gar Goei Loke, Qinshen Tang, Yangge Xiao +1Predict-Then-Optimize Learning to Optimize
Department of Management and Marketing, Durham University Business School, Waterside, Durham DH1 1SL, United Kingdom · Nanyang Business School, Nanyang Technological University, Singapore · Faculty of Business and Economics, The University of Melbourne +1
A Solver-Free Training Method for Predict-then-Optimize
Jun 17, 2026Beichen Wan, Mo LiuPredict-Then-Optimize Learning to Optimize
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, NC, USA.
Data-Driven Maintenance Optimization: Aligning Prognostic Learning with Decision Objective
Jun 24, 2025Zhuojun Xie, Adam Abdin, Yiping FangPredictive Maintenance Predict-Then-Optimize
Laboratoire Génie Industriel, CentraleSupélec, Université Paris-Saclay

Aug 15, 2026J/K move · Enter open · S save

Decision-Driven Regularization: A Blended Model for Learning and Optimization

Gar Goei Loke, Qinshen Tang, Yangge Xiao, Xun Zhang

Department of Management and Marketing, Durham University Business School, Waterside, Durham DH1 1SL, United Kingdom · Nanyang Business School, Nanyang Technological University, Singapore · Faculty of Business and Economics, The University of Melbourne+1

Predict-Then-Optimize Learning to Optimize Decision-Focused Learning

Open paper AskPDF arXiv

In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features. This context is common in many business applications ranging from on-demand delivery and retail operations to portfolio optimization and inventory management. In this paper, we study the learning and optimization approach, which first learns how outcomes result from the features, and then selects optimal decisions based on these outcomes. We focus on the integrated learning and optimization literature, and identify that a lack of control for prediction accuracy can lead to overfitting and a loss of decision effectiveness against simple separate learning and optimization models. Instead, we propose a bi-objective formulation that balances prediction accuracy and cost minimization, termed decision-driven regularization. It also addresses ambiguity in the definition of the cost function via a surrogate that depends on a new hyperparameter. We additionally show that alternative perspectives for formulating the problem, namely robust optimization and regret minimization, lead to models that are closely related to our proposed model. As a consequence, our framework generalizes models such as SPO+. Our model is shown to be numerically superior to other benchmarks, such as OLS, Random Forest, XGBoost, SPO+, Perturbation Gradient, and Learning and Rank, in our synthetic studies.

Abstract

Model Misspecification

Explore similar work

Decision-Driven Regularization: A Blended Model for Learning and Optimization

A Solver-Free Training Method for Predict-then-Optimize

Data-Driven Maintenance Optimization: Aligning Prognostic Learning with Decision Objective