# Byzantine Resilient Non-Convex SVRG with Distributed Batch Gradient Computations

arXiv: https://arxiv.org/abs/1912.04531 · HTML: https://mlsanity.com/paper/1912.04531/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [Fault-Tolerant Federated Reinforcement Learning with Theoretical Guarantee](https://mlsanity.com/paper/2110.14074/) (2021)
- [BROADCAST: Reducing Both Stochastic and Compression Noise to Robustify Communication-Efficient Federated Learning](https://mlsanity.com/paper/2104.06685/) (2021)
- [Bridging Differential Privacy and Byzantine-Robustness via Model Aggregation](https://mlsanity.com/paper/2205.00107/) (2022)
- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)
- [Byzantine-Robust Decentralized Stochastic Optimization with Stochastic Gradient Noise-Independent Learning Error](https://mlsanity.com/paper/2308.05292/) (2023)
- [Stochastic Alternating Direction Method of Multipliers for Byzantine-Robust Distributed Learning](https://mlsanity.com/paper/2106.06891/) (2021)

## Abstract (arXiv)

In this work, we consider the distributed stochastic optimization problem of minimizing a non-convex function f(x) = mathbbExi ~ 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 α-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 tildeOleft( frac1ε5/3 K2/3 + fracα4/3ε5/3 right) gradient computations on average at each node (SN and WNs) to reach an ε-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 α present in the network on the convergence performance of the algorithm.