With increasing real world applications of machine learning, models are often required to comply with certain domain based requirements, e.g., safety guarantees in aircraft systems, legal constraints in a loan approval model. A natural way to represent these properties is in the form of constraints. Including such constraints in machine learning is typically done by the means of regularization, which does not guarantee satisfaction of the constraints. In this paper, we present a machine learning approach that can handle a wide variety of constraints, and guarantee that these constraints will be satisfied by the model even on unseen data. We cast machine learning as a maximum satisfiability problem, and solve it using a novel algorithm SaDe which combines constraint satisfaction with gradient descent. We demonstrate on three use cases that this approach learns models that provably satisfy the given constraints.

翻译：随着机器学习在现实世界中的应用日益增长,往往需要模型来遵守某些基于领域的要求,例如飞机系统的安全保障、贷款批准模式中的法律限制。一种自然代表这些特性的方式是限制的形式。在机器学习中,这种限制通常通过正规化的方式进行,这并不能保证对各种限制的满足。在本文件中,我们提出了一个机器学习方法,可以处理各种限制,保证这些限制甚至以无形数据为模式得到满足。我们把机器学习当作一个最大限度的可诉性问题,并使用一种将限制满意度与梯度下降相结合的新型的Sade算法来解决这个问题。我们用三种方法来证明这种方法学习能够满足既定限制的模式。