Robust Experimental Design via Generalised Bayesian Inference

TL;DR

This paper introduces GBOED, a robust experimental design method based on generalized Bayesian inference, which improves resilience to model misspecification and outliers by using a loss-based update instead of traditional likelihoods.

Contribution

It extends Gibbs inference to experimental design, deriving a new acquisition function called Gibbs EIG that enhances robustness against noise and model errors.

Findings

GBOED improves robustness to outliers.

Gibbs EIG outperforms traditional methods in noisy settings.

The approach maintains effective information gain estimation.

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.