This paper addresses the challenge of achieving Differential Privacy (DP) in Federated Learning (FL) under the partial-participation setting, where each machine participates in only some of training rounds. While earlier work achieved optimal performance and efficiency in full-participation scenarios, these methods could not extend effectively to cases with partial-participation. Our approach addresses this gap by introducing a novel noise-cancellation mechanism that ensures privacy without compromising convergence rates or computational efficiency. We analyze our method within the Stochastic Convex Optimization (SCO) framework and demonstrate that it achieves optimal performance for both homogeneous and heterogeneous data distributions. This work broadens the applicability of DP in FL, providing a practical and efficient solution for privacy-preserving learning in distributed systems with partial participation.

This paper addresses the challenge of preserving privacy in Federated Learning (FL) within centralized systems, focusing on both trusted and untrusted server scenarios. We analyze this setting within the Stochastic Convex Optimization (SCO) framework, and devise methods that ensure Differential Privacy (DP) while maintaining optimal convergence rates for homogeneous and heterogeneous data distributions. Our approach, based on a recent stochastic optimization technique, offers linear computational complexity, comparable to non-private FL methods, and reduced gradient obfuscation. This work enhances the practicality of DP in FL, balancing privacy, efficiency, and robustness in a variety of server trust environments.