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

2026-05-30

AI Summary

This work addresses the challenge of infeasible optimization arising from hard constraints in imitation learning, which often leads to training instability. To this end, it introduces— for the first time—the augmented Lagrangian theory under infeasibility into imitation learning and proposes a hierarchical optimization framework. This framework automatically resolves constraint conflicts through infeasibility detection and adaptive constraint relaxation, guiding the policy toward the solution of the nearest feasible problem. The approach is evaluated in driving simulations involving constraints on total acceleration and pedestrian safety, where it successfully learns safe and stable policies. Experimental results demonstrate its effectiveness and robustness in naturally occurring infeasible scenarios.

Abstract

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.

Problem

• infeasible optimization
• imitation learning
• hard constraints
• training instability
• constrained policy learning

Innovation

• infeasible optimization
• augmented Lagrangian method
• imitation learning
• hard constraints
• closest-feasible solution