Dissecting the Impact of Model Misspecification in Data-Driven Optimization

2025-03-01

AI Summary

This paper investigates decision performance degradation in data-driven optimization under model misspecification. To address this problem, we develop a tail regret bound analysis framework grounded in higher-order asymptotic expansions and an improved Berry–Esseen theorem, applicable to both conventional estimation paradigms (e.g., maximum likelihood) and joint estimation-and-optimization learning. Our analysis is the first to establish that ensemble methods universally achieve a dual benefit under misspecification: enhanced statistical efficiency and improved robustness. The derived interpretable upper bound quantitatively characterizes the performance crossover points between these two paradigms, yielding the first theoretical criterion for decision-oriented model selection in finite-sample regimes. This result substantially broadens the credible applicability of machine learning in real-world optimization settings.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Impact of model misspecification in data-driven optimization
• Comparison of traditional vs integrated optimization approaches
• Performance under varying degrees of model misspecification

Innovation

• Integrated approach minimizes decision error
• Comparison via finite-sample tail regret bounds
• Higher-order expansions and Berry-Esseen theorem