In order to perform machine learning among multiple parties while protecting the privacy of raw data, privacy-preserving machine learning based on secure multi-party computation (MPL for short) has been a hot spot in recent. The configuration of MPL usually follows the peer-to-peer architecture, where each party has the same chance to reveal the output result. However, typical business scenarios often follow a hierarchical architecture where a powerful, usually \textit{privileged party}, leads the tasks of machine learning. Only the \textit{privileged party} can reveal the final model even if other \textit{assistant parties} collude with each other. It is even required to avoid the abort of machine learning to ensure the scheduled deadlines and/or save used computing resources when part of \textit{assistant parties} drop out. Motivated by the above scenarios, we propose \pmpl, a robust MPL framework with a \textit{privileged party}. \pmpl supports three-party training in the semi-honest setting. By setting alternate shares for the \textit{privileged party}, \pmpl is robust to tolerate one of the rest two parties dropping out during the training. With the above settings, we design a series of efficient protocols based on vector space secret sharing for \pmpl to bridge the gap between vector space secret sharing and machine learning. Finally, the experimental results show that the performance of \pmpl is promising when we compare it with the state-of-the-art MPL frameworks. Especially, in the LAN setting, \pmpl is around $16\times$ and $5\times$ faster than \texttt{TF-encrypted} (with \texttt{ABY3} as the back-end framework) for the linear regression, and logistic regression, respectively. Besides, the accuracy of trained models of linear regression, logistic regression, and BP neural networks can reach around 97\%, 99\%, and 96\% on MNIST dataset respectively.

翻译：为了在多个当事人中进行机器学习, 同时保护原始数据的隐私, 隐私保存机学习在安全的多方计算( MPL 短时间 MPL) 的基础上是最近的一个热点。 MPL 的配置通常遵循对等对等架构, 每个当事人都有同样的机会披露输出结果。 但是, 典型的商业情景往往遵循一个等级架构, 其中一个强大的, 通常是\ textit{ privited party} 领导机器学习的任务。 只有 ktrient demoit{ privied part} 才能显示最终模式。 liderit{ taltitude{ lider{ part} 才能显示最后模式。 lider lider{ previted} 的三方培训模式, 和 livertical commt 一起显示一个基于 ligialtal deal deal comml 的存储程序, 也可以显示一个基于 ligideal developmental development 的存储程序, 和两个基于 Excial developtal developtal 演示方之间的共享 。 我们 dal dal 演示方之间, 我们 dreal dretal dre dismodal dism 。