English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Many recent applications in machine learning and data fitting call for thealgorithmic solution of structured smooth convex optimization problems.Although the gradient descent method is a natural choice for this task, itrequires exact gradient computations and hence can be inefficient when theproblem size is large or the gradient is difficult to evaluate. Therefore,there has been much interest in inexact gradient methods (IGMs), in which anefficiently computable approximate gradient is used to perform the update ineach iteration. Currently, non-asymptotic linear convergence results for IGMsare typically established under the assumption that the objective function isstrongly convex, which is not satisfied in many applications of interest; whilelinear convergence results that do not require the strong convexity assumptionare usually asymptotic in nature. In this paper, we combine the best of thesetwo types of results and establish---under the standard assumption that thegradient approximation errors decrease linearly to zero---the non-asymptoticlinear convergence of IGMs when applied to a class of structured convexoptimization problems. Such a class covers settings where the objectivefunction is not necessarily strongly convex and includes the least squares andlogistic regression problems. We believe that our techniques will find furtherapplications in the non-asymptotic convergence analysis of other first-ordermethods.

Non-Asymptotic Convergence Analysis of Inexact Gradient Methods for Machine Learning Without Strong Convexity