Towards Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds. (arXiv:2201.10780v1 [stat.ML])

Web: http://arxiv.org/abs/2201.10780

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 \left( L_2 \delta + \gamma \delta^2 \right) $, where $ L_2 $ is the
Lipschitz constant for the Hessian, $ \gamma $ depends on both the …

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