5 papers
Gradient correlation is a key ingredient to accelerate SGD with momentum
Julien Hermant, Marien Renaud, Jean-François Aujol +2
Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pe…
Continuized Nesterov Momentum Achieves the Complexity in Smooth Nonconvex Optimization
Julien Hermant, Jean-François Aujol, Charles Dossal +3
For first-order optimization of non-convex functions with Lipschitz-continuous gradient and Hessian, the best-known complexity for reaching an -approximation of a stat…
Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case
Julien Hermant, Jean-François Aujol, Charles Dossal +1
We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show th…
Continuized Nesterov Acceleration for Non-Convex Optimization
Julien Hermant, Jean-François Aujol, Charles Dossal +2
In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is…
Heavy Ball Momentum for Non-Strongly Convex Optimization
Jean-François Aujol, Charles Dossal, Hippolyte Labarrière +1
When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time pa…