Show simple item record

dc.contributor.authorHanzely, Filip
dc.contributor.authorRichtarik, Peter
dc.date.accessioned2018-04-04T12:38:14Z
dc.date.available2018-04-04T12:38:14Z
dc.date.issued2018-03-20
dc.identifier.urihttp://hdl.handle.net/10754/627407
dc.description.abstractRelative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1803.07374v1
dc.relation.urlhttp://arxiv.org/pdf/1803.07374v1
dc.rightsArchived with thanks to arXiv
dc.titleFastest Rates for Stochastic Mirror Descent Methods
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer Science Program
dc.eprint.versionPre-print
dc.contributor.institutionMoscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia
dc.contributor.institutionUniversity of Edinburgh, Edinburgh, United Kingdom
dc.identifier.arxividarXiv:1803.07374
kaust.personHanzely, Filip
kaust.personRichtarik, Peter
refterms.dateFOA2018-06-13T17:32:27Z


Files in this item

Thumbnail
Name:
1803.07374v1.pdf
Size:
620.2Kb
Format:
PDF
Description:
Preprint

This item appears in the following Collection(s)

Show simple item record