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.

翻译：我们提出了一种方法论，用于在机器学习系统中通过识别和利用决策的效用结构来构建简化抽象。机器学习任务通常涉及高维输出空间（例如，为图像中的每个像素或图中的每个节点进行预测），尽管更粗粒度的输出通常足以满足下游决策需求（例如，图像的区域而非像素）。开发者常常手动设计输出空间的抽象，但存在大量可能的抽象方式，且模型的输出空间选择如何影响其在下游决策中的效用尚不明确。我们提出了一种自动配置输出空间的方法，以最小化决策相关信息损失。从几何视角出发，我们将算法的一个步骤表述为概率单纯形上的投影（称为折叠），该投影在H-熵意义上最小化决策相关信息的总体损失。关键的是，在抽象后的结果空间中进行学习所需数据更少，从而显著提升决策质量。我们在两个领域验证了该方法：深度神经网络训练的数据采集任务和闭环野火管理任务。