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GraSP-STL: A Graph-Based Framework for Zero-Shot Signal Temporal Logic Planning via Offline Goal-Conditioned Reinforcement Learning

Ancheng Hou, Ruijia Liu, Xiang Yin

Abstract

This paper studies offline, zero-shot planning under Signal Temporal Logic (STL) specifications. We assume access only to an offline dataset of state-action-state transitions collected by a task-agnostic behavior policy, with no analytical dynamics model, no further environment interaction, and no task-specific retraining. The objective is to synthesize a control strategy whose resulting trajectory satisfies an arbitrary unseen STL specification. To this end, we propose GraSP-STL, a graph-search-based framework for zero-shot STL planning from offline trajectories. The method learns a goal-conditioned value function from offline data and uses it to induce a finite-horizon reachability metric over the state space. Based on this metric, it constructs a directed graph abstraction whose nodes represent representative states and whose edges encode feasible short-horizon transitions. Planning is then formulated as a graph search over waypoint sequences, evaluated using arithmetic-geometric mean robustness and its interval semantics, and executed by a learned goal-conditioned policy. The proposed framework separates reusable reachability learning from task-conditioned planning, enabling zero-shot generalization to unseen STL tasks and long-horizon planning through the composition of short-horizon behaviors from offline data. Experimental results demonstrate its effectiveness on a range of offline STL planning tasks.

GraSP-STL: A Graph-Based Framework for Zero-Shot Signal Temporal Logic Planning via Offline Goal-Conditioned Reinforcement Learning

Abstract

This paper studies offline, zero-shot planning under Signal Temporal Logic (STL) specifications. We assume access only to an offline dataset of state-action-state transitions collected by a task-agnostic behavior policy, with no analytical dynamics model, no further environment interaction, and no task-specific retraining. The objective is to synthesize a control strategy whose resulting trajectory satisfies an arbitrary unseen STL specification. To this end, we propose GraSP-STL, a graph-search-based framework for zero-shot STL planning from offline trajectories. The method learns a goal-conditioned value function from offline data and uses it to induce a finite-horizon reachability metric over the state space. Based on this metric, it constructs a directed graph abstraction whose nodes represent representative states and whose edges encode feasible short-horizon transitions. Planning is then formulated as a graph search over waypoint sequences, evaluated using arithmetic-geometric mean robustness and its interval semantics, and executed by a learned goal-conditioned policy. The proposed framework separates reusable reachability learning from task-conditioned planning, enabling zero-shot generalization to unseen STL tasks and long-horizon planning through the composition of short-horizon behaviors from offline data. Experimental results demonstrate its effectiveness on a range of offline STL planning tasks.

Paper Structure

This paper contains 17 sections, 20 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model
  4. Signal Temporal Logic
  5. AGM Robustness and Interval Semantics
  6. Problem Formulation
  7. Overall Framework
  8. Goal-Conditioned Reachability Measure and Policy Learning
  9. Graph Construction
  10. Graph Search for STL Planning
  11. STL Robustness Evaluation
  12. Graph Search Procedure
  13. Experiments
  14. Experimental Setup
  15. Case Study
  16. ...and 2 more sections

Figures (3)

  • Figure 3: Overall framework of proposed GraSP-STL.
  • Figure 4: Experimental environment and reachability graph.
  • Figure 5: Case study of planning and execution.