Ideal Abstractions for Decision-Focused Learning
This addresses the challenge of designing effective abstractions for decision-focused learning, offering a novel approach to reduce data requirements and enhance utility in downstream tasks, though it appears incremental as it builds on existing geometric and entropy concepts.
The paper tackles the problem of high-dimensional output spaces in machine learning by proposing a method to automatically configure abstractions that minimize loss of decision-relevant information, demonstrating improved decision quality with less data in domains like deep neural network training and wildfire management.
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.