389 research outputs found
Stochastic Intermediate Gradient Method for Convex Problems with Inexact Stochastic Oracle
In this paper we introduce new methods for convex optimization problems with
inexact stochastic oracle. First method is an extension of the intermediate
gradient method proposed by Devolder, Glineur and Nesterov for problems with
inexact oracle. Our new method can be applied to the problems with composite
structure, stochastic inexact oracle and allows using non-Euclidean setup. We
prove estimates for mean rate of convergence and probabilities of large
deviations from this rate. Also we introduce two modifications of this method
for strongly convex problems. For the first modification we prove mean rate of
convergence estimates and for the second we prove estimates for large
deviations from the mean rate of convergence. All the rates give the complexity
estimates for proposed methods which up to multiplicative constant coincide
with lower complexity bound for the considered class of convex composite
optimization problems with stochastic inexact oracle
An Accelerated Method For Decentralized Distributed Stochastic Optimization Over Time-Varying Graphs
We consider a distributed stochastic optimization problem that is solved by a
decentralized network of agents with only local communication between
neighboring agents. The goal of the whole system is to minimize a global
objective function given as a sum of local objectives held by each agent. Each
local objective is defined as an expectation of a convex smooth random function
and the agent is allowed to sample stochastic gradients for this function. For
this setting we propose the first accelerated (in the sense of Nesterov's
acceleration) method that simultaneously attains optimal up to a logarithmic
factor communication and oracle complexity bounds for smooth strongly convex
distributed stochastic optimization. We also consider the case when the
communication graph is allowed to vary with time and obtain complexity bounds
for our algorithm, which are the first upper complexity bounds for this setting
in the literature
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