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Faster and Non-ergodic O(1/K) Stochastic Alternating Direction Method of Multipliers
Cong Fang · Feng Cheng · Zhouchen Lin

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #171 #None

We study stochastic convex optimization subjected to linear equality constraints. Traditional Stochastic Alternating Direction Method of Multipliers and its Nesterov's acceleration scheme can only achieve ergodic O(1/\sqrt{K}) convergence rates, where K is the number of iteration. By introducing Variance Reduction (VR) techniques, the convergence rates improve to ergodic O(1/K). In this paper, we propose a new stochastic ADMM which elaborately integrates Nesterov's extrapolation and VR techniques. With Nesterov’s extrapolation, our algorithm can achieve a non-ergodic O(1/K) convergence rate which is optimal for separable linearly constrained non-smooth convex problems, while the convergence rates of VR based ADMM methods are actually tight O(1/\sqrt{K}) in non-ergodic sense. To the best of our knowledge, this is the first work that achieves a truly accelerated, stochastic convergence rate for constrained convex problems. The experimental results demonstrate that our algorithm is significantly faster than the existing state-of-the-art stochastic ADMM methods.

Author Information

Cong Fang (Peking University)
Feng Cheng (Peking University)
Zhouchen Lin (Peking University)

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