Gradient based Bilevel for Inverse Optimal Control, a Riemannian approach

• URL: http://arxiv.org/abs/2606.10841v1
• Date: Tue, 09 Jun 2026 13:27:01 GMT
• Title: Gradient based Bilevel for Inverse Optimal Control, a Riemannian approach
• Abstract summary: Inverse Optimal Control (IOC) aims to recover the cost function that explains observed trajectories as solutions of an optimal control problem.<n>Recent projection-based approaches offer a promising alternative but suffer from numerical instability when solved with gradient-based methods.<n>We show that these difficulties stem from the geometric structure of the IOC feasible set.
• Score: 5.398550081886241
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• DRAFTO: Decoupled Reduced-space and Adaptive Feasibility-repair Trajectory Optimization for Robotic Manipulators [4.0407133618465005]
  This paper introduces a new algorithm for trajectory optimization, Decoupled Reduced-space and Adaptive Feasibility-repair Trajectory Optimization (DRAFTO)<n>To reduce the number of repeated constrained optimizations while handling joint-limit feasibility, the optimization is decoupled into a reduced-space Gauss-Newton (GN) descent.<n>The results of our benchmark tests against optimization-based planners, such as CHOMP, TrajOpt, GPMP2, and FACTO, validate the high efficiency and reliability across diverse scenarios and tasks.
  arXiv  Detail & Related papers  (2026-03-10T20:24:42Z)
• A Framework for Combining Optimization-Based and Analytic Inverse Kinematics [53.66628333687382]
  Twolytic and optimization methods for inverse kinematics (IK) problems have been deeply studied in the history of robotics.<n>We present a new formulation for IK avoidance that uses an IK solution that is fundamentally easier for ours to solve.
  arXiv  Detail & Related papers  (2026-02-04T22:23:32Z)
• Optimizing Optimizers for Fast Gradient-Based Learning [53.81268610971847]
  We lay the theoretical foundation for automating design in gradient-based learning.<n>By treating gradient loss signals as a function that translates to parameter motions, the problem reduces to a family of convex optimization problems.
  arXiv  Detail & Related papers  (2025-12-06T09:50:41Z)
• Preference Optimization for Combinatorial Optimization Problems [54.87466279363487]
  Reinforcement Learning (RL) has emerged as a powerful tool for neural optimization, enabling models learns that solve complex problems without requiring expert knowledge.<n>Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast action spaces.<n>We propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling.
  arXiv  Detail & Related papers  (2025-05-13T16:47:00Z)
• Towards Robust Spacecraft Trajectory Optimization via Transformers [17.073280827888226]
  We develop an autonomous generative model to solve non- optimal control problems in real-time.<n>We extend the capabilities of ART to address robust chance-constrained optimal control problems.<n>This work marks an initial step toward the reliable deployment of AI-driven solutions in safety-critical autonomous systems such as spacecraft.
  arXiv  Detail & Related papers  (2024-10-08T00:58:42Z)
• ODE-based Learning to Optimize [28.380622776436905]
  We present a comprehensive framework integrating the inertial systems with Hessian-driven damping equation (ISHD) We formulate a novel learning to optimize (L2O) problem aimed at minimizing the stopping time subject to the convergence and stability condition. Empirical validation of our framework is conducted through extensive numerical experiments across a diverse set of optimization problems.
  arXiv  Detail & Related papers  (2024-06-04T06:39:45Z)
• OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transport [51.6416022358349]
  sys is a framework that harnesses optimal transport theory for data repair under Conditional Independence (CI) constraints. We develop an iterative algorithm inspired by Sinkhorn's matrix scaling algorithm, which efficiently addresses high-dimensional and large-scale data.
  arXiv  Detail & Related papers  (2024-03-04T18:23:55Z)
• DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization [9.28162057044835]
  Optimal trajectory local is computationally expensive for nonlinear and high-dimensional dynamical systems. In this paper we introduce Diffu-based general model for non-dimensional optima problems. We also present Diff+, a novel constrained diffusion model with an additional loss in that further reduces the problem violations.
  arXiv  Detail & Related papers  (2024-02-22T03:52:17Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Robust expected improvement for Bayesian optimization [1.8130068086063336]
  We propose a surrogate modeling and active learning technique called robust expected improvement (REI) that ports adversarial methodology into the BO/GP framework. We illustrate and draw comparisons to several competitors on benchmark synthetic exercises and real problems of varying complexity.
  arXiv  Detail & Related papers  (2023-02-16T22:34:28Z)
• Quantum variational optimization: The role of entanglement and problem hardness [0.0]
  We study the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem. Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem's topology. We find evidence that applying conditional value at risk type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions.
  arXiv  Detail & Related papers  (2021-03-26T14:06:54Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.