6 papers · 1 filter
Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance
Daniel Cortild, Coralia Cartis
We investigate the Stochastic Krasnoselskii-Mann iterations for expected nonexpansive fixed-point problems in a real Hilbert space. We establish convergence guarantees under signif…
Bias-Optimal Bounds for SGD: A Computer-Aided Lyapunov Analysis
Daniel Cortild, Lucas Ketels, Juan Peypouquet +1
The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias com…
Regularization methods for solving hierarchical variational inequalities with complexity guarantees
Daniel Cortild, Meggie Marschner, Mathias Staudigl
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes…
Global Optimization Algorithm through High-Resolution Sampling
Daniel Cortild, Claire Delplancke, Nadia Oudjane +1
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potentia…
Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Guillaume Garrigos, Daniel Cortild, Lucas Ketels +1
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question…
Krasnoselskii-Mann Iterations: Inertia, Perturbations and Approximation
Daniel Cortild, Juan Peypouquet
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unifie…