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.
| Comments: | 19 Pages, 6 figures, 1 table. Submitted to IEEE Transactions on Automatic Control and is pending review |
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| MSC classes: | 65K10, 49M37 |
| Cite as: | arXiv:2602.00921 [math.OC] |
| (or arXiv:2602.00921v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2602.00921 arXiv-issued DOI via DataCite |
From: Eric Gelphman [view email]
[v1]
Sat, 31 Jan 2026 22:25:46 UTC (1,073 KB)
[v2]
Sat, 25 Apr 2026 02:50:03 UTC (1,054 KB)
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