Learning Temporal Logic Predicates from Data with Statistical Guarantees

TL;DR

This paper introduces a new method for learning temporal logic predicates from data that guarantees correctness with finite samples, using statistical techniques like conformal prediction, applicable in control and robotics.

Contribution

The paper presents a novel approach combining expression optimization and conformal prediction to learn temporally logical predicates with statistical correctness guarantees from data.

Findings

Effective on simulated trajectory data

Provides finite-sample correctness guarantees

Ablation studies highlight component contributions

Abstract

Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining motion planning among autonomous agents, and classifying data. However, existing methods for learning temporal logic predicates from data do not provide assurances about the correctness of the resulting predicate. We present a novel method to learn temporal logic predicates from data with finite-sample correctness guarantees. Our approach leverages expression optimization and conformal prediction to learn predicates that correctly describe future trajectories under mild statistical assumptions. We provide experimental results showing the performance of our approach on a simulated trajectory dataset and perform ablation studies to understand how each component of our algorithm contributes to its performance.