On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians
Provides theoretical justification and empirical evidence for JFB in high-dimensional optimal control, addressing a fundamental challenge in learning-based value function methods.
The paper proves convergence guarantees for Jacobian-Free Backpropagation (JFB) in stochastic minibatch settings for optimal control with implicit Hamiltonians, and demonstrates scalability on high-dimensional problems including multi-agent and swarm control.
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.