Learning Temporal Logic Predicates from Data with Statistical Guarantees

TL;DR

The paper tackles learning signal temporal logic predicates from trajectory data with finite-sample guarantees. It integrates expression optimization with conformal prediction to produce predicates along with valid robustness intervals for unseen trajectories, using interval arithmetic to compose predicates efficiently. Key contributions include a unified framework that yields nontrivial, interpretable STL predicates with statistical guarantees, plus ablation studies showing the benefits of TeLEx-like loss and triviality penalties. The approach demonstrates effectiveness on synthetic data and a real-world VRU dataset, highlighting potential for safety-critical verification and constraint-based motion planning in robotics with partial observations.

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.

Figures (6)

• Figure 1: Block diagram showing the sequence of components in our algorithm. Steps shaded in yellow are part of the dataset generation process. Blue represent prior work and green represents novel contributions.
• Figure 2: Comparison of the linear and TeLEx loss functions.
• Figure 3: Trajectory data.
• Figure 4: Example predicate $\phi^\star$ and confidence interval predictions for 40 randomly sampled trajectories from $\mathcal{D}_{\text{val}}$. We plot a scatterplot of predicted robustness values for each sample; the predicted intervals generated by $f^1_{\phi^\star}$ and $f^2_{\phi^\star}$; and the true robustness for each sample. The true robustness is shown in red if it lies outside the predicted conformal CI.
• Figure 5: Samples from the VRU dataset overlaid on 8 regions used to define STL atoms.