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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

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STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

A Catalyst Framework for Minimax Optimization

A Catalyst Framework for Minimax Optimization

Second-Order Guarantees In Federated Learning

Bulk and Surface Electronic Structure of the Dual-Topology Semimetal Pt2HgSe3

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Escaping from saddle points on Riemannian manifolds

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

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

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

A Catalyst Framework for Minimax Optimization

Second-Order Guarantees In Federated Learning

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

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

A Catalyst Framework for Minimax Optimization

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Bulk and Surface Electronic Structure of the Dual-Topology Semimetal Pt2HgSe3

Escaping from saddle points on Riemannian manifolds

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