Interpretable and Constrained Machine Learning via Combinatorial Optimization

Recent transformative advances in machine and deep learning have enabled the recognition of complex patterns from vast data, with or without human supervision. These advances have catalyzed the application of machine learning techniques to a diversity of problem settings, from healthcare to robotics. Unfortunately, sophisticated machine learning techniques can result in the construction of domain models that are challenging for humans to understand and in which it is difficult to enforce user-specified constraints. This lack of interpretability, as well as the inability to impose further constraints, has become a major obstacle to human trust in machine learning models and a challenge to the broad adoption of machine learning-based systems. While one of the goals of artificial intelligence is, arguably, to extend its reasoning beyond the cognitive capabilities of humankind, such a pursuit should not disregard human-compatibility. Interpretable machine learning aims to develop human-understandable models and to explain so-called black-box models. Constrained machine learning addresses the problem by enforcing expert knowledge and formal requirements on solutions. In this dissertation we introduce methods to produce machine learning models/artifacts that are interpretable and amenable to human-specified constraints. We do so through the exploitation of techniques for solving combinatorial optimization problems. In particular, we propose novel formulations to learn inherently interpretable models such as decision trees. Our work includes encoding a variety of solution formats and objectives. We further propose frameworks and encodings for the integration of constraints during or after training. We show that our approaches successfully produce high-quality interpretable and constrained solutions in short runtimes, solving new problems and improving the state of the art in others. Our collective work shows that interpretability does not necessarily come at the expense of quality and, in fact, sometimes improves it. Utilizing constraints can also improve accuracy despite reducing the space of feasible solutions. Lastly, we discuss how the work presented in this dissertation can be extended in several interesting directions and inspire new approaches for using combinatorial optimization problems in machine learning.

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