# The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspective

arXiv: https://arxiv.org/abs/2510.18215 · HTML: https://mlsanity.com/paper/2510.18215/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [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)
- [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)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [On the Differentiability of the Solution to Convex Optimization Problems](https://mlsanity.com/paper/1804.05098/) (2018)
- [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)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (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)
- [On the Impossibility of Statistically Improving Empirical Optimization: A Second-Order Stochastic Dominance Perspective](https://mlsanity.com/paper/2105.13419/) (2021)
- [Optimal Covariate Balancing Conditions in Propensity Score Estimation](https://mlsanity.com/paper/2108.01255/) (2021)
- [Model-based Offline Reinforcement Learning with Local Misspecification](https://mlsanity.com/paper/2301.11426/) (2023)
- [Minimizing Sensitivity to Model Misspecification](https://mlsanity.com/paper/1807.02161/) (2018)
- [Sensitivity Analysis using Approximate Moment Condition Models](https://mlsanity.com/paper/1808.07387/) (2018)
- [Inference in Dynamic Discrete Choice Problems under Local Misspecification](https://mlsanity.com/paper/1603.07987/) (2016)
- [On Misspecification in Prediction Problems and Robustness via Improper Learning](https://mlsanity.com/paper/2101.05234/) (2021)
- [Adapting to Misspecification](https://mlsanity.com/paper/2305.14265/) (2023)

## Built on by (most cited first, 3 of 3)

- [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 Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)

## Abstract (arXiv)

Data-driven stochastic optimization is ubiquitous in machine learning and operational decision-making problems. Sample average approximation (SAA) and model-based approaches such as estimate-then-optimize (ETO) or integrated estimation-optimization (IEO) are all popular, with model-based approaches being able to circumvent some of the issues with SAA in complex context-dependent problems. Yet the relative performance of these methods is poorly understood, with most results confined to the dichotomous cases of the model-based approach being either well-specified or misspecified. We develop the first results that allow for a more granular analysis of the relative performance of these methods under a local misspecification setting, which models the scenario where the model-based approach is nearly well-specified. By leveraging tools from contiguity theory in statistics, we show that there is a bias-variance tradeoff between SAA, IEO, and ETO under local misspecification, and that the relative importance of the bias and the variance depends on the degree of local misspecification. Moreover, we derive explicit expressions for the decision bias, which allows us to characterize (un)impactful misspecification directions, and provide further geometric understanding of the variance.