Develops AP particle schemes for Landau-Fokker-Planck and Dougherty operators using implicit JKO flows, inner-time quadrature, and neural network implementations that preserve structure in stiff regimes.
On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians
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abstract
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.
years
2026 2representative citing papers
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Asymptotic-preserving deterministic particle methods for collisional plasma models
Develops AP particle schemes for Landau-Fokker-Planck and Dougherty operators using implicit JKO flows, inner-time quadrature, and neural network implementations that preserve structure in stiff regimes.
- Implicit Neural Optimal Transport via Fixed-Point Optimization