69 research outputs found
Byzantine Stochastic Gradient Descent
This paper studies the problem of distributed stochastic optimization in an
adversarial setting where, out of the machines which allegedly compute
stochastic gradients every iteration, an -fraction are Byzantine, and
can behave arbitrarily and adversarially. Our main result is a variant of
stochastic gradient descent (SGD) which finds -approximate
minimizers of convex functions in iterations. In contrast, traditional
mini-batch SGD needs 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 sampling complexity and time
complexity
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