Robust Experimental Design via Generalised Bayesian Inference

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.

Performance Comparisons of Reinforcement Learning Algorithms for Sequential Experimental Design

Recent developments in sequential experimental design look to construct a policy that can efficiently navigate the design space, in a way that maximises the expected information gain. Whilst there is work on achieving tractable policies for experimental design problems, there is significantly less work on obtaining policies that are able to generalise well - i.e. able to give good performance despite a change in the underlying statistical properties of the experiments. Conducting experiments sequentially has recently brought about the use of reinforcement learning, where an agent is trained to navigate the design space to select the most informative designs for experimentation. However, there is still a lack of understanding about the benefits and drawbacks of using certain reinforcement learning algorithms to train these agents. In our work, we investigate several reinforcement learning algorithms and their efficacy in producing agents that take maximally informative design decisions in sequential experimental design scenarios. We find that agent performance is impacted depending on the algorithm used for training, and that particular algorithms, using dropout or ensemble approaches, empirically showcase attractive generalisation properties.