On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918467194585088 |
|---|---|
| author | Gelphman, Eric Verma, Deepanshu Yang, Nicole Tianjiao Osher, Stanley Fung, Samy Wu |
| author_facet | Gelphman, Eric Verma, Deepanshu Yang, Nicole Tianjiao Osher, Stanley Fung, Samy Wu |
| contents | Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit deep learning approach using Jacobian-Free Backpropagation (JFB) to address this setting, but only established sample-wise descent guarantees. In this paper, we establish convergence guarantees for JFB in the stochastic minibatch setting, showing that the resulting updates converge to stationary points of the expected optimal control objective. We further demonstrate scalability on substantially higher-dimensional problems, including multi-agent optimal consumption and swarm-based quadrotor and bicycle control. Together, our results provide both theoretical justification and empirical evidence for using JFB in high-dimensional optimal control with implicit Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians Gelphman, Eric Verma, Deepanshu Yang, Nicole Tianjiao Osher, Stanley Fung, Samy Wu Optimization and Control Machine Learning Numerical Analysis 65K10, 49M37 Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit deep learning approach using Jacobian-Free Backpropagation (JFB) to address this setting, but only established sample-wise descent guarantees. In this paper, we establish convergence guarantees for JFB in the stochastic minibatch setting, showing that the resulting updates converge to stationary points of the expected optimal control objective. We further demonstrate scalability on substantially higher-dimensional problems, including multi-agent optimal consumption and swarm-based quadrotor and bicycle control. Together, our results provide both theoretical justification and empirical evidence for using JFB in high-dimensional optimal control with implicit Hamiltonians. |
| title | On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians |
| topic | Optimization and Control Machine Learning Numerical Analysis 65K10, 49M37 |
| url | https://arxiv.org/abs/2602.00921 |