Time-Incremental Learning of Temporal Logic Classifiers Using Decision Trees

Real-time and human-interpretable decision-making in autonomous systems is a significant but challenging task, which usually requires predictions of possible future events from limited data. While machine learning techniques have achieved promising results in this field, they lack interpretability and the ability to make online predictions for sequential behaviors. In this paper, we introduce a time-incremental learning framework to predict the labels of time-series signals that are received incrementally over time, referred to as prefix signals. These signals are being observed as they are generated, and their time lengths are shorter than their corresponding time horizons. We present a novel decision tree-based approach to learn a finite number of Signal Temporal Logic (STL) specifications from a given dataset and construct a predictor based on them. Each STL specification serves as a binary classifier of the time-series data and captures a specific part of the dataset's temporal properties over time. The predictor is built by assigning time-variant weights to the STL formulas, which represent their classification impacts. The weights are learned using neural networks to minimize the misclassification rate of classifying prefix signals with different time lengths. The predictor is then used to predict the labels of prefix signals by computing the weighted sum of their robustnesses with respect to the STL formulas. The effectiveness and classification performance of our algorithm is evaluated on urban-driving and naval-surveillance case studies.