# Uncertainty-Aware Constraint Learning for Adaptive Safe Motion Planning from Demonstrations

arXiv: https://arxiv.org/abs/2011.04141 · HTML: https://mlsanity.com/paper/2011.04141/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

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

- [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)
- [Learning Soft Constraints From Constrained Expert Demonstrations](https://mlsanity.com/paper/2206.01311/) (2022)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (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)
- [Inverse Reinforcement Learning With Constraint Recovery](https://mlsanity.com/paper/2305.08130/) (2023)
- [Active Constraint Learning in High Dimensions from Demonstrations](https://mlsanity.com/paper/2512.22757/) (2025)

## Abstract (arXiv)

We present a method for learning to satisfy uncertain constraints from demonstrations. Our method uses robust optimization to obtain a belief over the potentially infinite set of possible constraints consistent with the demonstrations, and then uses this belief to plan trajectories that trade off performance with satisfying the possible constraints. We use these trajectories in a closed-loop policy that executes and replans using belief updates, which incorporate data gathered during execution. We derive guarantees on the accuracy of our constraint belief and probabilistic guarantees on plan safety. We present results on a 7-DOF arm and 12D quadrotor, showing our method can learn to satisfy high-dimensional (up to 30D) uncertain constraints, and outperforms baselines in safety and efficiency.