Accelerated iterative regularization via dual diagonal descent

Abstract

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we analyze both convergence and stability. Using tools from inexact proximal calculus, we prove early stopping results with optimal convergence rates for additive data-fit terms as well as more general cases, such as the Kullback-Leibler divergence, for which different type of proximal point approximations hold.

References in corpus (6)

• On the Complexity of Best Arm Identification in Multi-Armed Bandit Models
• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• Exploring Large Feature Spaces with Hierarchical Multiple Kernel Learning
• Iterative regularization via dual diagonal descent
• Don't relax: early stopping for convex regularization

Cited by in corpus (2)

• Convergence of the Forward-Backward Algorithm: Beyond the Worst Case with the Help of Geometry
• Theta-regularized Kriging: Modelling and Algorithms