An Accelerated First-Order Method for Non-convex Optimization on Manifolds
Graph Chatbot
Chattez avec Graph Search
Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.
AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.
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 ...
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 ...
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 ...
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 point ...
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 ...
For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj = -1j, uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the ...
We obtain quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm with target distribution in d-dimensional Euclidean space, showing that HMC mixes quickly whenever the target log-distribution is strongly concave and has ...
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 ...
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 ...
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 ...