Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs
A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross index sets, with gradients and Hessians contributing additional linear equations per sample and substantially reducing sample complexity compared to va...
| Authors | Matías Gómez-Aedo, Behzad Azmi, Yuyang Huang et al. |
|---|---|
| Primary category | math.OC |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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