A Theoretical Analysis of Efficiency Constrained Utility-Privacy Bi-Objective Optimization in Federated Learning

Federated learning (FL) enables multiple clients to collaboratively learn a shared model without sharing their individual data. Concerns about utility, privacy, and training efficiency in FL have garnered significant research attention. Differential privacy has emerged as a prevalent technique in FL, safeguarding the privacy of individual user data while impacting utility and training efficiency. Within Differential Privacy Federated Learning (DPFL), previous studies have primarily focused on the utility-privacy trade-off, neglecting training efficiency, which is crucial for timely completion. Moreover, differential privacy achieves privacy by introducing controlled randomness (noise) on selected clients in each communication round. Previous work has mainly examined the impact of noise level (<inline-formula><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula>) and communication rounds (<inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula>) on the privacy-utility dynamic, overlooking other influential factors like the sample ratio (<inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>, the proportion of selected clients). This paper systematically formulates an efficiency-constrained utility-privacy bi-objective optimization problem in DPFL, focusing on <inline-formula><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>. We provide a comprehensive theoretical analysis, yielding analytical solutions for the Pareto front. Extensive empirical experiments verify the validity and efficacy of our analysis, offering valuable guidance for low-cost parameter design in DPFL.