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    FedNL: Making Newton-Type Methods Applicable to Federated Learning

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    Type
    Preprint
    Authors
    Safaryan, Mher cc
    Islamov, Rustem
    Qian, Xun cc
    Richtarik, Peter cc
    KAUST Department
    Computer Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2021-06-05
    Permanent link to this record
    http://hdl.handle.net/10754/669462
    
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    Abstract
    Inspired by recent work of Islamov et al (2021), we propose a family of Federated Newton Learn (FedNL) methods, which we believe is a marked step in the direction of making second-order methods applicable to FL. In contrast to the aforementioned work, FedNL employs a different Hessian learning technique which i) enhances privacy as it does not rely on the training data to be revealed to the coordinating server, ii) makes it applicable beyond generalized linear models, and iii) provably works with general contractive compression operators for compressing the local Hessians, such as Top-$K$ or Rank-$R$, which are vastly superior in practice. Notably, we do not need to rely on error feedback for our methods to work with contractive compressors. Moreover, we develop FedNL-PP, FedNL-CR and FedNL-LS, which are variants of FedNL that support partial participation, and globalization via cubic regularization and line search, respectively, and FedNL-BC, which is a variant that can further benefit from bidirectional compression of gradients and models, i.e., smart uplink gradient and smart downlink model compression. We prove local convergence rates that are independent of the condition number, the number of training data points, and compression variance. Our communication efficient Hessian learning technique provably learns the Hessian at the optimum. Finally, we perform a variety of numerical experiments that show that our FedNL methods have state-of-the-art communication complexity when compared to key baselines.
    Publisher
    arXiv
    arXiv
    2106.02969
    Additional Links
    https://arxiv.org/pdf/2106.02969.pdf
    Collections
    Preprints; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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