Privacy and Byzantine resilience (BR) are two crucial requirements of modern-day distributed machine learning. The two concepts have been extensively studied individually but the question of how to combine them effectively remains unanswered. This paper contributes to addressing this question by studying the extent to which the distributed SGD algorithm, in the standard parameter-server architecture, can learn an accurate model despite (a) a fraction of the workers being malicious (Byzantine), and (b) the other fraction, whilst being honest, providing noisy information to the server to ensure differential privacy (DP). We first observe that the integration of standard practices in DP and BR is not straightforward. In fact, we show that many existing results on the convergence of distributed SGD under Byzantine faults, especially those relying on $(\alpha,f)$-Byzantine resilience, are rendered invalid when honest workers enforce DP. To circumvent this shortcoming, we revisit the theory of $(\alpha,f)$-BR to obtain an approximate convergence guarantee. Our analysis provides key insights on how to improve this guarantee through hyperparameter optimization. Essentially, our theoretical and empirical results show that (1) an imprudent combination of standard approaches to DP and BR might be fruitless, but (2) by carefully re-tuning the learning algorithm, we can obtain reasonable learning accuracy while simultaneously guaranteeing DP and BR.

本文研究了在标准参数服务器架构下，分布式 SGD 算法能否在部分节点受到 Byzantine 攻击，另一部分节点提供加噪的信息以保证 DP 的情况下，学习一个准确的模型。研究发现，在保证 DP 的情况下，现有的对于分布式 SGD 在 Byzantine 错误下的收敛性结果是无效的；通过重新调整学习算法，本文提供了关键性见解，基于 BR 的理论提供了近似收敛保证。

在分布式 SGD 中结合差分隐私和拜占庭容错