Dual-Free Stochastic Decentralized Optimization with Variance Reduction

Abstract

We consider the problem of training machine learning models on distributed data in a decentralized way. For finite-sum problems, fast single-machine algorithms for large datasets rely on stochastic updates combined with variance reduction. Yet, existing decentralized stochastic algorithms either do not obtain the full speedup allowed by stochastic updates, or require oracles that are more expensive than regular gradients. In this work, we introduce a Decentralized stochastic algorithm with Variance Reduction called DVR. DVR only requires computing stochastic gradients of the local functions, and is computationally as fast as a standard stochastic variance-reduced algorithms run on a $1/n$ fraction of the dataset, where $n$ is the number of nodes. To derive DVR, we use Bregman coordinate descent on a well-chosen dual problem, and obtain a dual-free algorithm using a specific Bregman divergence. We give an accelerated version of DVR based on the Catalyst framework, and illustrate its effectiveness with simulations on real data.

References in corpus (6)

• A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates
• Optimal algorithms for smooth and strongly convex distributed optimization in networks
• A Universal Catalyst for First-Order Optimization
• DSA: Decentralized Double Stochastic Averaging Gradient Algorithm
• SDCA without Duality, Regularization, and Individual Convexity
• Revisiting EXTRA for Smooth Distributed Optimization

Cited by in corpus (3)

• Variance Reduced EXTRA and DIGing and Their Optimal Acceleration for Strongly Convex Decentralized Optimization
• PMGT-VR: A decentralized proximal-gradient algorithmic framework with variance reduction
• Decentralized Composite Optimization with Compression