Publications related to Escaping from saddle points on Riemannian manifolds

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

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

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

Ali H. Sayed, Stefan Vlaski

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...

IEEE2020

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

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

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromi ...

2019

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

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

Boris Buffoni

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) x R-2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of ...

MATHEMATICAL SCIENCE PUBL2019

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Volkan Cevher, Ahmet Alacaoglu, Armin Eftekhari, Fabian Ricardo Latorre Gomez, Mehmet Fatih Sahin

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

2019

A central limit theorem for integrals of random waves

Marius Christopher Lemm, Matthew De Courcy-Ireland

We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbitrary dimension, thanks to the universality of the local Weyl law. The key te ...

2019

Escaping from saddle points on Riemannian manifolds

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Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

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

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

Renormalization of quantum field theory on Riemannian manifolds

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Some regularity results for p-harmonic mappings between Riemannian manifolds

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

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

A central limit theorem for integrals of random waves

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Renormalization of quantum field theory on Riemannian manifolds

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

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

A central limit theorem for integrals of random waves

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

Some regularity results for p-harmonic mappings between Riemannian manifolds

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

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

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