• Corpus ID: 246285569

Towards Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds

  title={Towards Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds},
  author={Tianyu Wang},
  • Tianyu Wang
  • Published 26 January 2022
  • Mathematics, Computer Science
  • ArXiv
We study Hessian estimators for real-valued functions defined over an n-dimensional complete Riemannian manifold. We introduce new stochastic zeroth-order Hessian estimators using O(1) function evaluations. We show that, for a smooth real-valued function f with Lipschitz Hessian (with respect to the Rimannian metric), our estimator achieves a bias bound of order O ( L2δ + γδ 2 ) , where L2 is the Lipschitz constant for the Hessian, γ depends on both the Levi-Civita connection and function f… 

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