  Federated learning (FL) is a new distributed learning paradigm, with privacy,
utility, and efficiency as its primary pillars. Existing research indicates
that it is unlikely to simultaneously attain infinitesimal privacy leakage,
utility loss, and efficiency. Therefore, how to find an optimal trade-off
solution is the key consideration when designing the FL algorithm. One common
way is to cast the trade-off problem as a multi-objective optimization problem,
i.e., the goal is to minimize the utility loss and efficiency reduction while
constraining the privacy leakage not exceeding a predefined value. However,
existing multi-objective optimization frameworks are very time-consuming, and
do not guarantee the existence of the Pareto frontier, this motivates us to
seek a solution to transform the multi-objective problem into a
single-objective problem because it is more efficient and easier to be solved.
To this end, we propose FedPAC, a unified framework that leverages PAC learning
to quantify multiple objectives in terms of sample complexity, such
quantification allows us to constrain the solution space of multiple objectives
to a shared dimension, so that it can be solved with the help of a
single-objective optimization algorithm. Specifically, we provide the results
and detailed analyses of how to quantify the utility loss, privacy leakage,
privacy-utility-efficiency trade-off, as well as the cost of the attacker from
the PAC learning perspective.
