signSGD with Majority Vote is Communication Efficient And Byzantine Fault Tolerant
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Training neural networks on large datasets can be accelerated by distributing the workload over a network of machines. As datasets grow ever larger, networks of hundreds or thousands of machines become economically viable. The time cost of communicating gradients limits the effectiveness of using such large machine counts, as may the increased chance of network faults. We explore a particularly simple algorithm for robust, communication-efficient learning---signSGD. Workers transmit only the sign of their gradient vector to a server, and the overall update is decided by a majority vote. This algorithm uses 32× less communication per iteration than full-precision, distributed SGD. Under natural conditions verified by experiment, we prove that signSGD converges in the large and mini-batch settings, establishing convergence for a parameter regime of Adam as a byproduct. We model adversaries as those workers who may compute a stochastic gradient estimate and manipulate it, but may not coordinate with other adversaries. Aggregating sign gradients by majority vote means that no individual worker has too much power. We prove that unlike SGD, majority vote is robust when up to 50 adversarially. On the practical side, we built our distributed training system in Pytorch. Benchmarking against the state of the art collective communications library (NCCL), our framework---with the parameter server housed entirely on one machine---led to a 25 when using 15 AWS p3.2xlarge machines.
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