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Byzantine Stochastic Gradient Descent

2020-02-17 | |  44 |   40 |   0

Abstract 

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of m machines which allegedly compute stochastic gradients every iteration, an image.png-fraction are Byzantine, and may behave adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds image.png-approximate minimizers of convex functions in image.png iterations. " m " In contrast, traditional mini-batch SGD needs image.png iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sample complexity and time complexity.

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