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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.
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with powerball method to accelerate. We show that the
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex optimization
In this work, we introduce ADAPD, $textbf{A}$ $textbf{D}$ecentr$textbf{A}$lized $textbf{P}$rimal-$textbf{D}$ual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. ADAPD makes
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject to linear c
The augmented Lagrangian method (ALM) is a fundamental tool for solving the canonical convex minimization problem with linear constraints, and efficiently and easily how to implement the original ALM is affirmatively significant. Recently, He and Yua