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Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Test de la dérivée première

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Principal Component Analysis By Optimization Of Symmetric Functions Has No Spurious Local Optima

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

Optimal Spline Generators for Derivative Sampling

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Escaping from saddle points on Riemannian manifolds

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Estimation of Phase and Its Higher Order Derivatives from a Single Complex Interferogram

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

Principal Component Analysis By Optimization Of Symmetric Functions Has No Spurious Local Optima

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Estimation of Phase and Its Higher Order Derivatives from a Single Complex Interferogram

Optimal Spline Generators for Derivative Sampling

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Escaping from saddle points on Riemannian manifolds