Publications related to Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Sylvain Calinon

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotic ...

2020

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Escaping from saddle points on Riemannian manifolds

Nicolas Henri Bernard Flammarion, Yue Sun

We consider minimizing a nonconvex, smooth function f on a Riemannian manifold 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 points on the manif ...

2019

Renormalization of quantum field theory on Riemannian manifolds

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...

2019

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

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Some regularity results for p-harmonic mappings between Riemannian manifolds

Changyu Guo

Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an eleme ...

2019

Averaging Stochastic Gradient Descent on Riemannian Manifolds

Nicolas Henri Bernard Flammarion

We propose an estimator for the mean of a random vector in Rd that can be computed in time O(n3.5 + n2d) for n i.i.d. samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has ...

2018

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

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An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Continuation Methods For Riemannian Optimization

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Adaptive Gradient Descent without Descent

Escaping from saddle points on Riemannian manifolds

Renormalization of quantum field theory on Riemannian manifolds

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

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Some regularity results for p-harmonic mappings between Riemannian manifolds

Averaging Stochastic Gradient Descent on Riemannian Manifolds

Some regularity results for p-harmonic mappings between Riemannian manifolds

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Renormalization of quantum field theory on Riemannian manifolds

Escaping from saddle points on Riemannian manifolds

Adaptive Gradient Descent without Descent

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Continuation Methods For Riemannian Optimization

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Averaging Stochastic Gradient Descent on Riemannian Manifolds

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