New method uses Hessian data to improve optimal control approximations

Researchers have developed a novel data-driven method for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. This approach utilizes the Pontryagin Maximum Principle to generate training data, including values, gradients, and Hessians of the value function. By augmenting weighted least-squares regression with this second-order information, the method significantly reduces sample complexity compared to value-only regression. The technique has been validated on problems of increasing state dimension, demonstrating improved approximation accuracy and closed-loop performance, with a substantial reduction in required training samples. AI

IMPACT This research could lead to more efficient and accurate solutions for complex control problems, potentially impacting fields that rely on optimization and dynamic systems.

RANK_REASON The cluster contains a single academic paper detailing a new method for solving complex mathematical problems. [lever_c_demoted from research: ic=1 ai=0.4]

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• arXiv
• Hamilton-Jacobi-Bellman PDEs
• Hessian-augmented Supervised Learning
• Pontryagin Maximum Principle

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