Learning Temporal Logic Predicates from Data with Statistical Guarantees

2024-06-15

arXiv.org

AI Summary

Existing temporal logic predicate learning methods lack finite-sample correctness guarantees, limiting their applicability in safety-critical tasks. This paper addresses trajectory data and proposes the first temporal logic (LTL/STL) predicate learning framework with finite-sample statistical guarantees. Our method integrates symbolic expression optimization with conformal prediction to theoretically ensure generalization reliability of learned predicates on unseen trajectories. Uncertainty is rigorously modeled via statistical learning theory, and statistical guarantees are explicitly embedded into the predicate structure search process. Experiments on synthetic trajectory data demonstrate high learning accuracy. Ablation studies confirm that the coupled mechanism of conformal calibration and optimization is decisive for achieving both statistical validity and effective satisfaction of classification or planning constraints.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Learning temporal logic predicates with statistical guarantees
• Ensuring correctness of predicates for future trajectory data
• Combining expression optimization and conformal prediction

Innovation

• Learning temporal logic predicates with guarantees
• Combining expression optimization and conformal prediction
• Ensuring correctness under mild statistical assumptions