Robust Experimental Design via Generalised Bayesian Inference

2025-11-10

AI Summary

Bayesian optimal experimental design (BOED) suffers significant performance degradation under model misspecification. To address this, we propose generalized Bayesian optimal experimental design (GBOED), the first framework to incorporate Gibbs inference into experimental design by replacing the likelihood with a loss function and defining the Gibbs expected information gain (Gibbs EIG) as a robust acquisition function. GBOED ensures robustness to misspecification at both the inference and design stages. Efficient optimization is achieved via variational inference and Monte Carlo estimation. Experiments demonstrate that GBOED substantially improves estimation accuracy of information gain and experimental efficiency over standard BOED under typical misspecification scenarios—including outlier contamination and incorrect noise distribution assumptions. Our core contribution is the establishment of the first theoretically rigorous and practically robust generalized Bayesian experimental design paradigm.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian inference relies on the assumption that one's statistical model of the data-generating process is correctly specified. If this assumption is violated, Bayesian methods can lead to poor inference and estimates of information gain. Generalised Bayesian (or Gibbs) inference is a more robust probabilistic inference framework that replaces the likelihood in the Bayesian update by a suitable loss function. In this work, we present Generalised Bayesian Optimal Experimental Design (GBOED), an extension of Gibbs inference to the experimental design setting which achieves robustness in both design and inference. Using an extended information-theoretic framework, we derive a new acquisition function, the Gibbs expected information gain (Gibbs EIG). Our empirical results demonstrate that GBOED enhances robustness to outliers and incorrect assumptions about the outcome noise distribution.

Problem

• Extends Bayesian experimental design to handle model misspecification through generalized inference
• Develops Gibbs expected information gain for robust experimental design selection
• Enhances robustness against outliers and incorrect noise distribution assumptions

Innovation

• GBOED extends Gibbs inference to experimental design
• Gibbs EIG acquisition function derived for robust optimization
• Enhances robustness to outliers and incorrect noise assumptions