  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/many objectives, such
as maximizing model performance, minimizing privacy leakage and training cost,
and being robust to malicious attacks. Multi-Objective Optimization (MOO)
aiming to optimize multiple conflicting objectives at the same time is quite
suitable for solving the optimization problem of Trustworthy Federated Learning
(TFL). In this paper, 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 works 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, for effectively and
efficiently finding Pareto optimal solutions, and we provide theoretical
analysis on their convergence. We design specific measurements of privacy
leakage, utility loss, and training cost for three privacy protection
mechanisms: Randomization, BatchCrypt (An efficient version of homomorphic
encryption), and Sparsification. Empirical experiments conducted under each of
the three protection mechanisms demonstrate the effectiveness of our proposed
algorithms.
