  The real-world testing of decisions made using causal machine learning models
is an essential prerequisite for their successful application. We focus on
evaluating and improving contextual treatment assignment decisions: these are
personalised treatments applied to e.g. customers, each with their own
contextual information, with the aim of maximising a reward. In this paper we
introduce a model-agnostic framework for gathering data to evaluate and improve
contextual decision making through Bayesian Experimental Design. Specifically,
our method is used for the data-efficient evaluation of the regret of past
treatment assignments. Unlike approaches such as A/B testing, our method avoids
assigning treatments that are known to be highly sub-optimal, whilst engaging
in some exploration to gather pertinent information. We achieve this by
introducing an information-based design objective, which we optimise
end-to-end. Our method applies to discrete and continuous treatments. Comparing
our information-theoretic approach to baselines in several simulation studies
demonstrates the superior performance of our proposed approach.
