The privacy-preserving federated learning for vertically partitioned data has
shown promising results as the solution of the emerging multi-party joint
modeling application, in which the data holders (such as government branches,
private finance and e-business companies) collaborate throughout the learning
process rather than relying on a trusted third party to hold data. However,
existing federated learning algorithms for vertically partitioned data are
limited to synchronous computation. To improve the efficiency when the
unbalanced computation/communication resources are common among the parties in
the federated learning system, it is essential to develop asynchronous training
algorithms for vertically partitioned data while keeping the data privacy. In
this paper, we propose an asynchronous federated SGD (AFSGD-VP) algorithm and
its SVRG and SAGA variants on the vertically partitioned data. Moreover, we
provide the convergence analyses of AFSGD-VP and its SVRG and SAGA variants
under the condition of strong convexity. We also discuss their model privacy,
data privacy, computational complexities and communication costs. To the best
of our knowledge, AFSGD-VP and its SVRG and SAGA variants are the first
asynchronous federated learning algorithms for vertically partitioned data.
Extensive experimental results on a variety of vertically partitioned datasets
not only verify the theoretical results of AFSGD-VP and its SVRG and SAGA
variants, but also show that our algorithms have much higher efficiency than
the corresponding synchronous algorithms.

本文提出了针对垂直分割数据的异步联邦学习算法 AFSGD-VP 及其 SVRG 和 SAGA 变体，并在强凸条件下提供了收敛性分析。实验结果验证了本算法的理论结果，并表明我们的算法比相应的同步算法效率高得多，并且具有模型隐私保护。

多方纵向协作学习隐私保护异步联邦学习算法

Privacy-Preserving Asynchronous Federated Learning Algorithms for  Multi-Party Vertically Collaborative Learning

In a lot of real-world data mining and machine learning applications, data
are provided by multiple providers and each maintains private records of
different feature sets about common entities. It is challenging to train these
vertically partitioned data effectively and efficiently while keeping data
privacy for traditional data mining and machine learning algorithms. In this
paper, we focus on nonlinear learning with kernels, and propose a federated
doubly stochastic kernel learning (FDSKL) algorithm for vertically partitioned
data. Specifically, we use random features to approximate the kernel mapping
function and use doubly stochastic gradients to update the solutions, which are
all computed federatedly without the disclosure of data. Importantly, we prove
that FDSKL has a sublinear convergence rate, and can guarantee the data
security under the semi-honest assumption. Extensive experimental results on a
variety of benchmark datasets show that FDSKL is significantly faster than
state-of-the-art federated learning methods when dealing with kernels, while
retaining the similar generalization performance.

本论文提出了一种名为 FDSKL 的算法，该算法使用随机特征来近似内核映射函数并使用双随机梯度更新解决方案，旨在高效地学习垂直分割的数据而保持数据安全和隐私。实验结果表明，该算法在处理内核时比现有的联合学习方法更快，并保留了类似的泛化性能。