# Learning Parametric Constraints in High Dimensions from Demonstrations

arXiv: https://arxiv.org/abs/1910.03477 · HTML: https://mlsanity.com/paper/1910.03477/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2019.

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

- [Benchmarking Constraint Inference in Inverse Reinforcement Learning](https://mlsanity.com/paper/2206.09670/) (2022)
- [Maximum Likelihood Constraint Inference from Stochastic Demonstrations](https://mlsanity.com/paper/2102.12554/) (2021)
- [Learning Soft Constraints From Constrained Expert Demonstrations](https://mlsanity.com/paper/2206.01311/) (2022)
- [A Comprehensive Survey on Inverse Constrained Reinforcement Learning: Definitions, Progress and Challenges](https://mlsanity.com/paper/2409.07569/) (2024)
- [Maximum Causal Entropy Inverse Constrained Reinforcement Learning](https://mlsanity.com/paper/2305.02857/) (2023)
- [Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations](https://mlsanity.com/paper/2112.04612/) (2021)
- [Confidence Aware Inverse Constrained Reinforcement Learning](https://mlsanity.com/paper/2406.16782/) (2024)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [Active Constraint Learning in High Dimensions from Demonstrations](https://mlsanity.com/paper/2512.22757/) (2025)
- [Watch, Infer, Coordinate: Inferring Robot Partner Constraints for Zero-Shot Coordination](https://mlsanity.com/paper/2610.02170/) (2026)

## Abstract (arXiv)

We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation's parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.