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

arXiv: https://arxiv.org/abs/2603.29533 · HTML: https://mlsanity.com/paper/2603.29533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Placed in

- Offline RL and imitation learning from data / [Robot learning from demonstration](https://mlsanity.com/offlinerl/robot-learning-from-demonstration/)

## Builds on (most cited first, 16 of 16)

- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [HIQL: Offline Goal-Conditioned RL with Latent States as Actions](https://mlsanity.com/paper/2307.11949/) (2023)
- [Tractable Reinforcement Learning of Signal Temporal Logic Objectives](https://mlsanity.com/paper/2001.09467/) (2020)
- [Multi-agent Motion Planning from Signal Temporal Logic Specifications](https://mlsanity.com/paper/2201.05247/) (2022)
- [Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1903.05186/) (2019)
- [Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables](https://mlsanity.com/paper/2204.06367/) (2022)
- [Signal Temporal Logic Neural Predictive Control](https://mlsanity.com/paper/2309.05131/) (2023)
- [Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges](https://mlsanity.com/paper/2402.13075/) (2024)
- [Graph-Assisted Stitching for Offline Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2506.07744/) (2025)
- [Funnel-based Reward Shaping for Signal Temporal Logic Tasks in Reinforcement Learning](https://mlsanity.com/paper/2212.03181/) (2022)
- [Robust-Locomotion-by-Logic: Perturbation-Resilient Bipedal Locomotion via Signal Temporal Logic Guided Model Predictive Control](https://mlsanity.com/paper/2403.15993/) (2024)
- [Test-Time Graph Search for Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2510.07257/) (2025)
- [STL2vec: Signal Temporal Logic Embeddings for Control Synthesis With Recurrent Neural Networks](https://mlsanity.com/paper/2109.04636/) (2021)
- [Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specifications](https://mlsanity.com/paper/2306.06808/) (2023)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [RRTη: Sampling-based Motion Planning and Control from STL Specifications using Arithmetic-Geometric Mean Robustness](https://mlsanity.com/paper/2602.16825/) (2026)

## Abstract (arXiv)

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.