  We present a methodology for formulating simplifying abstractions in machine
learning systems by identifying and harnessing the utility structure of
decisions. Machine learning tasks commonly involve high-dimensional output
spaces (e.g., predictions for every pixel in an image or node in a graph), even
though a coarser output would often suffice for downstream decision-making
(e.g., regions of an image instead of pixels). Developers often hand-engineer
abstractions of the output space, but numerous abstractions are possible and it
is unclear how the choice of output space for a model impacts its usefulness in
downstream decision-making. We propose a method that configures the output
space automatically in order to minimize the loss of decision-relevant
information. Taking a geometric perspective, we formulate a step of the
algorithm as a projection of the probability simplex, termed fold, that
minimizes the total loss of decision-related information in the H-entropy
sense. Crucially, learning in the abstracted outcome space requires less data,
leading to a net improvement in decision quality. We demonstrate the method in
two domains: data acquisition for deep neural network training and a
closed-loop wildfire management task.
