Publications related to Optimal control of geodesics in Riemannian manifolds

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

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

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

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

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

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

Nicolas Henri Bernard Flammarion

We consider the minimization of a function deﬁned on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...

2017

Detecting Anisotropic Inclusions Through EIT

Jan Cristina

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

Springer2017

An Approach for Imitation Learning on Riemannian Manifolds

Sylvain Calinon

In imitation learning, multivariate Gaussians are widely used to encode robot behaviors. Such approaches do not provide the ability to properly represent end-effector orientation, as the distance metric in the space of orientations is not Euclidean. In thi ...

2017

Y Stability and performance verification of optimization-based controllers

Colin Neil Jones, Milan Korda

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include g ...

Pergamon-Elsevier Science Ltd2017

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Simultaneous and proportional control of a prosthetic hand and wrist is still a controversial issue, although giant steps have lately been made in this direction. In this paper, we study the application of a novel machine learning method to the problem, wi ...

2017

Optimal control of geodesics in Riemannian manifolds

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Escaping from saddle points on Riemannian manifolds

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

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

Some regularity results for p-harmonic mappings between Riemannian manifolds

A central limit theorem for integrals of random waves

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

Detecting Anisotropic Inclusions Through EIT

An Approach for Imitation Learning on Riemannian Manifolds

Y Stability and performance verification of optimization-based controllers

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

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

Escaping from saddle points on Riemannian manifolds

Some regularity results for p-harmonic mappings between Riemannian manifolds

Detecting Anisotropic Inclusions Through EIT

An Approach for Imitation Learning on Riemannian Manifolds

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

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

Y Stability and performance verification of optimization-based controllers

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

A central limit theorem for integrals of random waves