Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

Darina Dvinskikh, Alexander Gasnikov

2021Journal of Inverse and Ill-Posed Problems32 citationsDOI

Abstract

Abstract We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

Topics & Concepts

OracleMathematical optimizationSmoothnessDual (grammatical number)Computer scienceNode (physics)LogarithmConvex optimizationStochastic programmingInverseStochastic optimizationRegular polygonMathematicsStructural engineeringMathematical analysisGeometrySoftware engineeringLiteratureArtEngineeringStochastic Gradient Optimization TechniquesSparse and Compressive Sensing TechniquesDistributed Control Multi-Agent Systems