[Paper Review] Inferring Temporal Logic Properties from Data using Boosted Decision Trees

Erfan Aasi, Cristian-Ioan Vasile+2 more|arXiv (Cornell University)|May 24, 2021

Bayesian Modeling and Causal Inference27 references4 citations

TL;DR

This paper introduces a novel boosted decision tree (BDT) framework for learning interpretable Signal Temporal Logic (STL) formulae and predictors from time-series data, enabling real-time, incremental prediction of signal labels from partially observed (prefix) signals. The method achieves higher prediction accuracy and better runtime scalability than prior work, particularly in autonomous driving and naval surveillance applications, with improved early anomaly detection capabilities.

ABSTRACT

Many autonomous systems, such as robots and self-driving cars, involve real-time decision making in complex environments, and require prediction of future outcomes from limited data. Moreover, their decisions are increasingly required to be interpretable to humans for safe and trustworthy co-existence. This paper is a first step towards interpretable learning-based robot control. We introduce a novel learning problem, called incremental formula and predictor learning, to generate binary classifiers with temporal logic structure from time-series data. The classifiers are represented as pairs of Signal Temporal Logic (STL) formulae and predictors for their satisfaction. The incremental property provides prediction of labels for prefix signals that are revealed over time. We propose a boosted decision-tree algorithm that leverages weak, but computationally inexpensive, learners to increase prediction and runtime performance. The effectiveness and classification accuracy of our algorithms are evaluated on autonomous-driving and naval surveillance case studies.

Motivation & Objective

• To address the challenge of real-time decision-making in robotics, where actions must be taken before full signal observation, by enabling early prediction of signal labels from incomplete data.
• To develop an interpretable learning-based control framework that combines formal temporal logic (STL) with machine learning for human-trustworthy robot decisions.
• To formulate and solve an incremental learning problem that predicts satisfaction of STL formulae on prefix signals as they are revealed over time.
• To improve prediction accuracy and runtime efficiency over existing methods by leveraging a boosted decision tree approach with exact MILP optimization for formula synthesis.
• To evaluate the framework on real-world robotics scenarios, including autonomous driving and naval surveillance, demonstrating its practical utility in anomaly detection.

Proposed method

• The framework learns a pair of (STL formula, predictor function) as a binary classifier, where the formula defines a logical property and the predictor estimates its satisfaction from partial signals.
• A boosted decision tree (BDT) algorithm combines weak learners—bounded-depth decision trees—using adaptive weighting, similar to AdaBoost, to improve overall prediction accuracy.
• At each tree node, an exact mixed-integer linear programming (MILP) formulation is used to compute the STL formula with minimum impurity, ensuring optimal formula synthesis at each split.
• The incremental learning variant dynamically updates the model as new signal data arrives, enabling real-time predictions before signal completion, with a heuristic to trigger updates based on signal progress.
• The offline version processes complete signals, while the incremental version supports early prediction by evaluating signal prefixes, crucial for time-critical applications.
• The method is evaluated using 5- and 10-fold cross-validation and compared against prior work, with performance measured via misclassification rate (MCR), incremental MCR (IMCR), and runtime.

Experimental results

Research questions

• RQ1 Can a learning framework predict the satisfaction of temporal logic properties from incomplete, time-ordered signals in real time?
• RQ2 How can interpretable, logic-based classifiers be automatically synthesized from time-series data to support human-understandable robot decisions?
• RQ3 What is the performance gain of using boosted decision trees with MILP-optimized STL formulae over existing methods in terms of prediction accuracy and runtime?
• RQ4 How does incremental learning compare to offline learning in early anomaly detection tasks, particularly in autonomous driving and naval surveillance?
• RQ5 Can the proposed BDT-based method scale efficiently while maintaining low misclassification rates, especially under overfitting risks in deep trees?

Key findings

• The proposed offline algorithm achieved a 12% relative improvement in misclassification rate (MCR) over [6] in 5-fold cross-validation and a 7% improvement in 10-fold cross-validation.
• In the incremental learning setting, the model reduced incremental MCR (IMCR) to 38.34% compared to 48.24% for the offline method, demonstrating superior early prediction capability.
• The incremental model achieved a 10% improvement in prediction accuracy over the offline method in the naval surveillance case study, enabling earlier detection of anomalous vessel behavior.
• The MILP-based formula optimization outperformed PSO in early tree depths (depth=1), but showed higher overfitting risk in deeper trees (depth=3), with a 1.45% MCR in training vs. 1.75% in test for MILP, indicating potential overfitting.
• Despite being slower than single-tree methods, the BDT framework scaled better with increasing tree count, with a total offline runtime of 1h7m for incremental learning and 8 minutes for offline learning, confirming its practical feasibility.
• The method demonstrated linearly improving prediction power over time in the incremental setting, with MCR decreasing steadily as more signal data became available, supporting reliable real-time inference.