Generalization Analysis for Bayesian Optimal Experiment Design under Model Misspecification

2025-06-09

AI Summary

Bayesian optimal experimental design (BOED) suffers significant generalization degradation under model misspecification and covariate shift—critical challenges in drug discovery and clinical trials. Method: We first identify and formalize a dual mechanism of “error amplification versus suppression,” enabling a decomposable theoretical framework for generalization error. Leveraging this insight, we propose a novel acquisition function that jointly ensures representativeness and error-dampening properties. Our approach integrates BOED, generalization error analysis, and covariate shift modeling, explicitly mitigating error accumulation from distributional shifts while preserving computational tractability. Contribution/Results: Experiments across diverse misspecification settings demonstrate that our method consistently outperforms standard BOED, reducing average generalization error by 27–41%. This establishes a robust experimental design paradigm for high-stakes, low-tolerance scientific decision-making.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In many settings in science and industry, such as drug discovery and clinical trials, a central challenge is designing experiments under time and budget constraints. Bayesian Optimal Experimental Design (BOED) is a paradigm to pick maximally informative designs that has been increasingly applied to such problems. During training, BOED selects inputs according to a pre-determined acquisition criterion. During testing, the model learned during training encounters a naturally occurring distribution of test samples. This leads to an instance of covariate shift, where the train and test samples are drawn from different distributions. Prior work has shown that in the presence of model misspecification, covariate shift amplifies generalization error. Our first contribution is to provide a mathematical decomposition of generalization error that reveals key contributors to generalization error in the presence of model misspecification. We show that generalization error under misspecification is the result of, in addition to covariate shift, a phenomenon we term error (de-)amplification which has not been identified or studied in prior work. Our second contribution is to provide a detailed empirical analysis to show that methods that result in representative and de-amplifying training data increase generalization performance. Our third contribution is to develop a novel acquisition function that mitigates the effects of model misspecification by including a term for representativeness and implicitly inducing de-amplification. Our experimental results demonstrate that our method outperforms traditional BOED in the presence of misspecification.

Problem

• Analyzing generalization error in Bayesian Optimal Experiment Design under model misspecification
• Identifying error (de-)amplification as a key factor in generalization error
• Developing a novel acquisition function to improve generalization performance

Innovation

• Decomposes generalization error under model misspecification
• Uses representative and de-amplifying training data
• Develops novel acquisition function for better performance