# Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrations

arXiv: https://arxiv.org/abs/2206.04632 · HTML: https://mlsanity.com/paper/2206.04632/

## Key facts

- Cited by 10 papers in the map (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 59 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## 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)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning to Generalize Across Long-Horizon Tasks from Human Demonstrations](https://mlsanity.com/paper/2003.06085/) (2020)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Multi-Level Discovery of Deep Options](https://mlsanity.com/paper/1703.08294/) (2017)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems](https://mlsanity.com/paper/2003.11500/) (2020)
- [Elaborating on Learned Demonstrations with Temporal Logic Specifications](https://mlsanity.com/paper/2002.00784/) (2020)
- [Modeling Long-horizon Tasks as Sequential Interaction Landscapes](https://mlsanity.com/paper/2006.04843/) (2020)
- [Interpretable Apprenticeship Learning with Temporal Logic Specifications](https://mlsanity.com/paper/1710.10532/) (2017)
- [Reactive Task and Motion Planning under Temporal Logic Specifications](https://mlsanity.com/paper/2103.14464/) (2021)

## Built on by (most cited first, 10 of 10)

- [Learning Neuro-Symbolic Skills for Bilevel Planning](https://mlsanity.com/paper/2206.10680/) (2022)
- [Inference-Time Policy Steering through Human Interactions](https://mlsanity.com/paper/2411.16627/) (2024)
- [Grounding Language Plans in Demonstrations Through Counterfactual Perturbations](https://mlsanity.com/paper/2403.17124/) (2024)
- [Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies](https://mlsanity.com/paper/2309.01884/) (2023)
- [Multimodal and Force-Matched Imitation Learning with a See-Through Visuotactile Sensor](https://mlsanity.com/paper/2311.01248/) (2023)
- [RecoveryChaining: Learning Local Recovery Policies for Robust Manipulation](https://mlsanity.com/paper/2410.13979/) (2024)
- [Diffusion Meets Options: Hierarchical Generative Skill Composition for Temporally-Extended Tasks](https://mlsanity.com/paper/2410.02389/) (2024)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Logic Learning from Demonstrations for Multi-step Manipulation Tasks in Dynamic Environments](https://mlsanity.com/paper/2404.16138/) (2024)
- [Structured Imitation Learning of Interactive Policies through Inverse Games](https://mlsanity.com/paper/2511.12848/) (2025)

## Abstract (arXiv)

Learning from demonstration (LfD) has succeeded in tasks featuring a long time horizon. However, when the problem complexity also includes human-in-the-loop perturbations, state-of-the-art approaches do not guarantee the successful reproduction of a task. In this work, we identify the roots of this challenge as the failure of a learned continuous policy to satisfy the discrete plan implicit in the demonstration. By utilizing modes (rather than subgoals) as the discrete abstraction and motion policies with both mode invariance and goal reachability properties, we prove our learned continuous policy can simulate any discrete plan specified by a linear temporal logic (LTL) formula. Consequently, an imitator is robust to both task- and motion-level perturbations and guaranteed to achieve task success. Project page: https://yanweiw.github.io/tli/