On Distributed Stochastic Gradient Descent For Nonconvex Functions In The Presence Of Byzantines

We consider the distributed stochastic optimization problem of minimizing a nonconvex function f in an adversarial setting. All the w worker nodes in the network are expected to send their stochastic gradient vectors to the fusion center (or server). However, some (at most alpha-fraction) of the nodes may be Byzantines, which may send arbitrary vectors instead. Vanilla implementation of distributed stochastic gradient descent (SGD) cannot handle such misbehavior from the nodes. We propose a robust variant of distributed SGD which is resilient to the presence of Byzantines. The fusion center employs a novel filtering rule that identifies and removes the Byzantine nodes. We show that T = (O) over tilde (1/wc(2) + alpha(2)/c(2)) iterations are needed to achieve an epsilon-approximate stationary point (x such that parallel to del f(x)parallel to(2) <= epsilon) for the nonconvex learning problem. Unlike other existing approaches, the proposed algorithm is independent of the problem dimension.