# Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty

arXiv: https://arxiv.org/abs/2001.09336 · HTML: https://mlsanity.com/paper/2001.09336/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2020.

## Built on by (most cited first, 12 of 12)

- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Data-Efficient Learning of Natural Language to Linear Temporal Logic Translators for Robot Task Specification](https://mlsanity.com/paper/2303.08006/) (2023)
- [Learning Safety Constraints from Demonstrations with Unknown Rewards](https://mlsanity.com/paper/2305.16147/) (2023)
- [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)
- [Generalizing Cooperative Eco-driving via Multi-residual Task Learning](https://mlsanity.com/paper/2403.04232/) (2024)
- [Automated Controller Calibration by Kalman Filtering](https://mlsanity.com/paper/2111.10832/) (2021)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [Positive-Unlabeled Constraint Learning for Inferring Nonlinear Continuous Constraints Functions from Expert Demonstrations](https://mlsanity.com/paper/2408.01622/) (2024)
- [Active Constraint Learning in High Dimensions from Demonstrations](https://mlsanity.com/paper/2512.22757/) (2025)
- [Failing Gracefully: Mitigating Impact of Inevitable Robot Failures](https://mlsanity.com/paper/2608.05313/) (2026)

## Abstract (arXiv)

We present an algorithm for learning parametric constraints from locally-optimal demonstrations, where the cost function being optimized is uncertain to the learner. Our method uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the demonstrations within a mixed integer linear program (MILP) to learn constraints which are consistent with the local optimality of the demonstrations, by either using a known constraint parameterization or by incrementally growing a parameterization that is consistent with the demonstrations. We provide theoretical guarantees on the conservativeness of the recovered safe/unsafe sets and analyze the limits of constraint learnability when using locally-optimal demonstrations. We evaluate our method on high-dimensional constraints and systems by learning constraints for 7-DOF arm and quadrotor examples, show that it outperforms competing constraint-learning approaches, and can be effectively used to plan new constraint-satisfying trajectories in the environment.