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SUMMARY:Computer-aided worst-case analyses and design of first-order metho
 ds for convex optimization - Adrien Taylor (INRIA Paris)
DTSTART:20200212T140000Z
DTEND:20200212T150000Z
UID:TALK137176@talks.cam.ac.uk
CONTACT:Hamza Fawzi
DESCRIPTION:In this presentation\, we will provide a high-level overview o
 f recent approaches for analyzing and designing first-order methods using 
 symbolic computations and/or semidefinite programming. A particular emphas
 is will be given to the "performance estimation" approach\, which enjoys c
 omfortable tightness guarantees: the approach fails only when the target r
 esults are impossible to prove. In particular\, it allows obtaining (tight
 ) worst-case guarantees for fixed-step first-order methods involving a var
 iety of oracles - that includes explicit\, projected\, proximal\, conditio
 nal\, mirror\, inexact\, or stochastic (sub)gradient steps - and a variety
  of convergence measures.\n\nThe presentation will be example-based\, as t
 he main ingredients necessary for understanding the methodologies are alre
 ady present in the analysis of the vanilla gradient method. For convincing
  the audience\, we will provide other examples that include analyses of th
 e Douglas-Rachford splitting\, and of a variant of the celebrated conjugat
 e gradient method.\n\nThe methodology is implemented within the package "P
 ESTO" (for "Performance EStimation TOolbox"\, available at https://github.
 com/AdrienTaylor/Performance-Estimation-Toolbox)\, which allows using the 
 framework without any tedious semidefinite programming modelling step.\n\n
 This talk are based on joint works with great collaborators (who will be m
 entioned during the presentation).
LOCATION:MR11  Centre for Mathematical Sciences
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