  In this paper we propose a method for the optimal allocation of observations
between an intrinsically explainable glass box model and a black box model. An
optimal allocation being defined as one which, for any given explainability
level (i.e. the proportion of observations for which the explainable model is
the prediction function), maximizes the performance of the ensemble on the
underlying task, and maximizes performance of the explainable model on the
observations allocated to it, subject to the maximal ensemble performance
condition. The proposed method is shown to produce such explainability optimal
allocations on a benchmark suite of tabular datasets across a variety of
explainable and black box model types. These learned allocations are found to
consistently maintain ensemble performance at very high explainability levels
(explaining $74\%$ of observations on average), and in some cases even
outperforming both the component explainable and black box models while
improving explainability.
