# Learning Constraints from Demonstrations

arXiv: https://arxiv.org/abs/1812.07084 · HTML: https://mlsanity.com/paper/1812.07084/

## Key facts

- Cited by 9 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.
- First posted on arXiv 17 Dec 2018.

## Placed in

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

## Built on by (most cited first, 9 of 9)

- [Data-Efficient Learning of Natural Language to Linear Temporal Logic Translators for Robot Task Specification](https://mlsanity.com/paper/2303.08006/) (2023)
- [Benchmarking Constraint Inference in Inverse Reinforcement Learning](https://mlsanity.com/paper/2206.09670/) (2022)
- [Safe Value Functions](https://mlsanity.com/paper/2105.12204/) (2021)
- [Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations](https://mlsanity.com/paper/2112.04612/) (2021)
- [Learning Preferences for Interactive Autonomy](https://mlsanity.com/paper/2210.10899/) (2022)
- [X-MEN: Guaranteed XOR-Maximum Entropy Constrained Inverse Reinforcement Learning](https://mlsanity.com/paper/2203.11842/) (2022)
- [How To Not Drive: Learning Driving Constraints from Demonstration](https://mlsanity.com/paper/2110.00645/) (2021)
- [Inferring Lexicographically-Ordered Rewards from Preferences](https://mlsanity.com/paper/2202.10153/) (2022)
- [DIAL: Distribution-Informed Adaptive Learning of Multi-Task Constraints for Safety-Critical Systems](https://mlsanity.com/paper/2501.18086/) (2025)

## Abstract (arXiv)

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. We also provide theoretical analysis on what subset of the constraint can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.