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.

翻译：联邦学习是一种新型分布式学习范式，其核心支柱为隐私性、效用性和效率。现有研究表明，同时实现无穷小的隐私泄露、效用损失和效率提升几乎是不可行的。因此，在联邦学习算法设计中，如何寻求最优折衷方案是关键考量。常见方法是将折衷问题转化为多目标优化问题，即在隐私泄露不超过预设值的约束下，最小化效用损失和效率下降。然而，现有的大多数多目标优化框架不仅耗时巨大，而且无法保证帕累托前沿的存在性，这促使我们寻求一种将多目标问题转化为单目标问题的解决方案，因为后者更高效且更易求解。为此，我们提出FedPAC——一种利用PAC学习从样本复杂度角度量化多个目标的统一框架。这种量化方式允许我们将多个目标的解空间约束至同一维度，从而借助单目标优化算法进行求解。具体而言，我们提供了从PAC学习视角量化效用损失、隐私泄露、隐私-效用-效率折衷以及攻击者成本的结果与详细分析。