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The privacy-preserving federated learning for vertically partitioned data hasshown promising results as the solution of the emerging multi-party jointmodeling application, in which the data holders (such as government branches,private finance and e-business companies) collaborate throughout the learningprocess rather than relying on a trusted third party to hold data. However,existing federated learning algorithms for vertically partitioned data arelimited to synchronous computation. To improve the efficiency when theunbalanced computation/communication resources are common among the parties inthe federated learning system, it is essential to develop asynchronous trainingalgorithms for vertically partitioned data while keeping the data privacy. Inthis paper, we propose an asynchronous federated SGD (AFSGD-VP) algorithm andits SVRG and SAGA variants on the vertically partitioned data. Moreover, weprovide the convergence analyses of AFSGD-VP and its SVRG and SAGA variantsunder the condition of strong convexity. We also discuss their model privacy,data privacy, computational complexities and communication costs. To the bestof our knowledge, AFSGD-VP and its SVRG and SAGA variants are the firstasynchronous federated learning algorithms for vertically partitioned data.Extensive experimental results on a variety of vertically partitioned datasetsnot only verify the theoretical results of AFSGD-VP and its SVRG and SAGAvariants, but also show that our algorithms have much higher efficiency thanthe corresponding synchronous algorithms.

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