Optimizing Privacy, Utility, and Efficiency in a Constrained Multi-Objective Federated Learning Framework

Conventionally, federated learning aims to optimize a single objective, typically the utility. However, for a federated learning system to be trustworthy, it needs to simultaneously satisfy multiple objectives, such as maximizing model performance, minimizing privacy leakage and training costs, and being robust to malicious attacks. Multi-Objective Optimization (MOO) aiming to optimize multiple conflicting objectives simultaneously is quite suitable for solving the optimization problem of Trustworthy Federated Learning (TFL). In this article, we unify MOO and TFL by formulating the problem of constrained multi-objective federated learning (CMOFL). Under this formulation, existing MOO algorithms can be adapted to TFL straightforwardly. Different from existing CMOFL algorithms focusing on utility, efficiency, fairness, and robustness, we consider optimizing privacy leakage along with utility loss and training cost, the three primary objectives of a TFL system. We develop two improved CMOFL algorithms based on NSGA-II and PSL, respectively, to effectively and efficiently find Pareto optimal solutions and provide theoretical analysis on their convergence. We design quantitative measurements of privacy leakage, utility loss, and training cost for three privacy protection mechanisms: Randomization, BatchCrypt (an efficient homomorphic encryption), and Sparsification. Empirical experiments conducted under the three protection mechanisms demonstrate the effectiveness of our proposed algorithms.