Learning Optimal Signal Temporal Logic Decision Trees for Classification: A Max-Flow MILP Formulation

This paper presents a novel framework for inferring timed temporal logic properties from data. The dataset comprises pairs of finite-time system traces and corresponding labels, denoting whether the traces demonstrate specific desired behaviors, e.g. whether the ship follows a safe route or not. Our proposed approach leverages decision-tree-based methods to infer Signal Temporal Logic classifiers using primitive formulae. We formulate the inference process as a mixed integer linear programming optimization problem, recursively generating constraints to determine both data classification and tree structure. Applying a max-flow algorithm on the resultant tree transforms the problem into a global optimization challenge, leading to improved classification rates compared to prior methodologies. Moreover, we introduce a technique to reduce the number of constraints by exploiting the symmetry inherent in STL primitives, which enhances the algorithm's time performance and interpretability. To assess our algorithm's effectiveness and classification performance, we conduct three case studies involving two-class, multi-class, and complex formula classification scenarios.