8 papers
Accelerated Stochastic Zeroth-Order Quasar-Convex Optimization
Eméric Gbaguidi, Julien Hermant
We consider unconstrained minimization of smooth quasar-convex functions when only noisy function evaluations are accessible through a stochastic zeroth-order oracle. For these non…
Acceleration for Polyak-Łojasiewicz Functions with a Gradient Aiming Condition
Julien Hermant
It is known that when minimizing smooth Polyak-Łojasiewicz (PL) functions, momentum algorithms cannot significantly improve the convergence bound of gradient descent, contrasting w…
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…
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…
Provably Accelerated Imaging with Restarted Inertia and Score-based Image Priors
Marien Renaud, Julien Hermant, Deliang Wei +1
Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization b…
Convergence Analysis of a Proximal Stochastic Denoising Regularization Algorithm
Marien Renaud, Julien Hermant, Nicolas Papadakis
Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to recover a clean image from a degraded observation. These algorithms are kno…
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…
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…