Gradient based Bilevel for Inverse Optimal Control, a Riemannian approach

2026-06-09

AI Summary

This work addresses the high computational cost of traditional bilevel optimization in inverse optimal control and the numerical instability of projection-based gradient methods, which often arise from constraint qualification failures. The study establishes, for the first time, that the set of feasible trajectories forms a smooth manifold, thereby reformulating the problem as an optimization task over this manifold. Building on this insight, the authors propose a feasibility-preserving Riemannian inverse optimal control method that integrates Riemannian optimization with the intrinsic geometric structure of the manifold. This approach ensures numerical stability while substantially improving computational efficiency. Experiments on real human arm movement data demonstrate that the proposed method reduces computation time by approximately fourfold compared to classical bilevel optimization, achieving comparable or superior reconstruction accuracy.

Abstract

Inverse Optimal Control (IOC) aims to recover the cost function that explains observed trajectories as solutions of an optimal control problem. Classical IOC formulations rely on bilevel optimization, which repeatedly solves a nested optimal control problem and quickly becomes computationally prohibitive for realistic systems. Recent projection-based approaches offer a promising alternative but suffer from numerical instability when solved with gradient-based methods due to violations of standard constraint qualifications. In this paper, we show that these difficulties stem from the geometric structure of the IOC feasible set. We demonstrate that the set of trajectories satisfying the optimality conditions naturally forms a manifold and reformulate IOC as an optimization problem on this manifold. Based on this insight, we propose a Riemannian Inverse Optimal Control (RIOC) method that projects observed trajectories onto the manifold of optimal solutions while preserving feasibility by construction. Experiments on real human arm trajectories show that the proposed method achieves comparable or better reconstruction accuracy than classical bilevel IOC while reducing computation time by about a factor of four. These results highlight the potential of geometric optimization methods to improve the scalability and reliability of IOC for robotics and human motion analysis.

Problem

• Inverse Optimal Control
• Bilevel Optimization
• Numerical Instability
• Constraint Qualifications
• Trajectory Reconstruction

Innovation

• Riemannian optimization
• Inverse Optimal Control
• manifold structure
• bilevel optimization
• geometric optimization