  A plethora of modern machine learning tasks require the utilization of
large-scale distributed clusters as a critical component of the training
pipeline. However, abnormal Byzantine behavior of the worker nodes can derail
the training and compromise the quality of the inference. Such behavior can be
attributed to unintentional system malfunctions or orchestrated attacks; as a
result, some nodes may return arbitrary results to the parameter server (PS)
that coordinates the training. Recent work considers a wide range of attack
models and has explored robust aggregation and/or computational redundancy to
correct the distorted gradients.
  In this work, we consider attack models ranging from strong ones: $q$
omniscient adversaries with full knowledge of the defense protocol that can
change from iteration to iteration to weak ones: $q$ randomly chosen
adversaries with limited collusion abilities which only change every few
iterations at a time. Our algorithms rely on redundant task assignments coupled
with detection of adversarial behavior. We also show the convergence of our
method to the optimal point under common assumptions and settings considered in
literature. For strong attacks, we demonstrate a reduction in the fraction of
distorted gradients ranging from 16%-99% as compared to the prior
state-of-the-art. Our top-1 classification accuracy results on the CIFAR-10
data set demonstrate 25% advantage in accuracy (averaged over strong and weak
scenarios) under the most sophisticated attacks compared to state-of-the-art
methods.
