# Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning

arXiv: https://arxiv.org/abs/2606.00730 · HTML: https://mlsanity.com/paper/2606.00730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 5 of its 8 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 5 of 5)

- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions](https://mlsanity.com/paper/2212.11365/) (2022)
- [Differentiable Constrained Imitation Learning for Robot Motion Planning and Control](https://mlsanity.com/paper/2210.11796/) (2022)
- [EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance](https://mlsanity.com/paper/2103.00452/) (2021)
- [The Augmented Lagrangian Method Can Approximately Solve Convex Optimization with Least Constraint Violation](https://mlsanity.com/paper/2111.06194/) (2021)

## Abstract (arXiv)

Imitation learning (IL) is an effective approach to train complex robotics policies. Recent works have introduced hard constraints into imitation-learning optimization problems to ensure safety, stability, and robustness of the learned policy. However, we argue that these constraints are sometimes infeasible, which can lead to unstable or difficult training dynamics. We study a simple remedy for such situations based on recent theoretical results on the augmented Lagrangian method in infeasible settings. We show that our approach drives the learned policy toward the solution of a closest-feasible constrained IL problem with desirable properties. The method is illustrated on a toy driving example with a total-acceleration constraint and pedestrian-safety constraints, a setting in which infeasibility can naturally arise while still allowing a safe learned policy.