Federated learning (FL) enables participating parties to collaboratively build a global model with boosted utility without disclosing private data information. Appropriate protection mechanisms have to be adopted to fulfill the opposing requirements in preserving \textit{privacy} and maintaining high model \textit{utility}. In addition, it is a mandate for a federated learning system to achieve high \textit{efficiency} in order to enable large-scale model training and deployment. We propose a unified federated learning framework that reconciles horizontal and vertical federated learning. Based on this framework, we formulate and quantify the trade-offs between privacy leakage, utility loss, and efficiency reduction, which leads us to the No-Free-Lunch (NFL) theorem for the federated learning system. NFL indicates that it is unrealistic to expect an FL algorithm to simultaneously provide excellent privacy, utility, and efficiency in certain scenarios. We then analyze the lower bounds for the privacy leakage, utility loss and efficiency reduction for several widely-adopted protection mechanisms including \textit{Randomization}, \textit{Homomorphic Encryption}, \textit{Secret Sharing} and \textit{Compression}. Our analysis could serve as a guide for selecting protection parameters to meet particular requirements.

翻译：联邦学习(FL)使参与方能够合作构建一个全球模式,在不披露私人数据信息的情况下提高效用;必须采用适当的保护机制,以满足在保存\ textit{privacy}和保持高模量{textit{plity}方面的相反要求;此外,联邦学习系统的任务是实现高写率{效率},以便能够进行大规模的示范培训和部署;我们提议一个统一的联邦学习框架,调和横向和纵向联合学习;根据这个框架,我们制定并量化隐私泄漏、效用损失和效率降低之间的权衡,这导致我们找到联邦学习系统的无自由Lunch(NFL)理论;NFL表示,期望FL算法同时提供极好的隐私、效用和效率是不现实的;然后,我们分析若干广泛采用的保护机制的隐私泄漏、效用损失和效率降低的较低界限,包括\ textimation{Randemization}、Textitriit{Homistric}能够选择我们安全文本和版本的特定分析。