mlsanityData to 14 Oct 2026

On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians

arXiv 2602.00921 ↗First posted 31 Jan 2026math.OC cs.LG cs.NAcited by 1

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Abstract (arXiv)

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~citegelphman2025end 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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 41 of its 54 references that are in the map. First posted on arXiv 31 Jan 2026.

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41 of 54 references.

References · 41

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  1. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0