Federated learning (FL) is a distributed machine learning (ML) framework where multiple clients collaborate to train a model without exposing their private data. FL involves cycles of local computations and bi-directional communications between the clients and server. To bolster data security during this process, FL algorithms frequently employ a differential privacy (DP) mechanism that introduces noise into each client's model updates before sharing. However, while enhancing privacy, the DP mechanism often hampers convergence performance. In this paper, we posit that an optimal balance exists between the number of local steps and communication rounds, one that maximizes the convergence performance within a given privacy budget. Specifically, we present a proof for the optimal number of local steps and communication rounds that enhance the convergence bounds of the DP version of the ScaffNew algorithm. Our findings reveal a direct correlation between the optimal number of local steps, communication rounds, and a set of variables, e.g the DP privacy budget and other problem parameters, specifically in the context of strongly convex optimization. We furthermore provide empirical evidence to validate our theoretical findings.

翻译：联邦学习（FL）是一种分布式机器学习（ML）框架，多个客户端协作训练模型而无需暴露其私有数据。FL涉及客户端与服务器之间的局部计算循环和双向通信。在此过程中为加强数据安全性，FL算法常采用差分隐私（DP）机制，在共享前向每个客户端的模型更新中注入噪声。然而，在增强隐私的同时，DP机制往往阻碍收敛性能。本文提出，在给定隐私预算下，局部步骤数与通信轮次之间存在最优平衡，能最大化收敛性能。具体而言，我们给出了ScaffNew算法DP版本中提升收敛界限的最优局部步骤数与通信轮次的证明。研究结果表明，在强凸优化场景下，最优局部步骤数、通信轮次与DP隐私预算及其他问题参数之间存在直接关联。我们进一步提供实证证据验证理论发现。