The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspective
This provides theoretical insights for machine learning and operational decision-making, but it is incremental as it extends existing analysis to a more granular setting.
The paper tackles the problem of understanding the relative performance of data-driven optimization methods like SAA, ETO, and IEO under local misspecification, showing there is a bias-variance tradeoff where bias and variance depend on the degree of misspecification, with explicit expressions derived for decision bias.
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.