A Formal Kinetic Theory for Zeroth-Order Newton Dynamics:Stein-Corrected Hessian Estimation and Curvature--Variance Trade-offs

Shihao Ji, Mingyu Li, Zihui Song

Zeroth-order Newton-type methods are useful when gradients and Hessians are unavailable, but they behave quite differently from first-order gradient-free methods. We develop a kine…