# Fast Stochastic Alternating Direction Method of Multipliers

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Wenliang Zhong,
James Kwok
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Proceedings of the 31st International Conference on Machine Learning, PMLR 32(1):46-54, 2014.

#### Abstract

We propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as existing stochastic ADMM algorithms, it improves the convergence rate on convex problems from \mO(1/\sqrtT) to \mO(1/T), where T is the number of iterations. This matches the convergence rate of the batch ADMM algorithm, but without the need to visit all the samples in each iteration. Experiments on the graph-guided fused lasso demonstrate that the new algorithm is significantly faster than state-of-the-art stochastic and batch ADMM algorithms.

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