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In this work, we consider the distributed stochastic optimization problem of minimizing a non-convex function $f(x) = mathbb{E}_{xi sim mathcal{D}} f(x; xi)$ in an adversarial setting, where the individual functions $f(x; xi)$ can also be potentially non-convex. We assume that at most $alpha$-fraction of a total of $K$ nodes can be Byzantines. We propose a robust stochastic variance-reduced gradient (SVRG) like algorithm for the problem, where the batch gradients are computed at the worker nodes (WNs) and the stochastic gradients are computed at the server node (SN). For the non-convex optimization problem, we show that we need $tilde{O}left( frac{1}{epsilon^{5/3} K^{2/3}} + frac{alpha^{4/3}}{epsilon^{5/3}} right)$ gradient computations on average at each node (SN and WNs) to reach an $epsilon$-stationary point. The proposed algorithm guarantees convergence via the design of a novel Byzantine filtering rule which is independent of the problem dimension. Importantly, we capture the effect of the fraction of Byzantine nodes $alpha$ present in the network on the convergence performance of the algorithm.
We study adversary-resilient stochastic distributed optimization, in which $m$ machines can independently compute stochastic gradients, and cooperate to jointly optimize over their local objective functions. However, an $alpha$-fraction of the machin
Decentralized optimization techniques are increasingly being used to learn machine learning models from data distributed over multiple locations without gathering the data at any one location. Unfortunately, methods that are designed for faultless ne
In this work, we consider the resilience of distributed algorithms based on stochastic gradient descent (SGD) in distributed learning with potentially Byzantine attackers, who could send arbitrary information to the parameter server to disrupt the tr
In this work, we propose a distributed algorithm for stochastic non-convex optimization. We consider a worker-server architecture where a set of $K$ worker nodes (WNs) in collaboration with a server node (SN) jointly aim to minimize a global, potenti
Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require synchronizatio