Byzantine-Resilient Non-Convex Stochastic Gradient Descent

• URL: http://arxiv.org/abs/2012.14368v2
• Date: Fri, 2 Apr 2021 17:25:48 GMT
• Title: Byzantine-Resilient Non-Convex Stochastic Gradient Descent
• Authors: Zeyuan Allen-Zhu, Faeze Ebrahimian, Jerry Li, Dan Alistarh
• Abstract summary: adversary-resilient distributed optimization, in which. machines can independently compute gradients, and cooperate. Our algorithm is based on a new concentration technique, and its sample complexity. It is very practical: it improves upon the performance of all prior methods when no. setting machines are present.
• Score: 61.6382287971982
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study adversary-resilient stochastic distributed optimization, in which $m$ machines can independently compute stochastic gradients, and cooperate to jointly optimize over their local objective functions. However, an $\alpha$-fraction of the machines are $\textit{Byzantine}$, in that they may behave in arbitrary, adversarial ways. We consider a variant of this procedure in the challenging $\textit{non-convex}$ case. Our main result is a new algorithm SafeguardSGD which can provably escape saddle points and find approximate local minima of the non-convex objective. The algorithm is based on a new concentration filtering technique, and its sample and time complexity bounds match the best known theoretical bounds in the stochastic, distributed setting when no Byzantine machines are present. Our algorithm is very practical: it improves upon the performance of all prior methods when training deep neural networks, it is relatively lightweight, and it is the first method to withstand two recently-proposed Byzantine attacks.

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