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FedNL: Making Newton-Type Methods Applicable to Federated Learning
Mher Safaryan · Rustem Islamov · Xun Qian · Peter Richtarik

Tue Jul 19 11:05 AM -- 11:10 AM (PDT) @ Room 318 - 320
Inspired by recent work of Islamov et al (2021), we propose a family of Federated Newton Learn (\algname{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, \algname{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 \algname{FedNL-PP}, \algname{FedNL-CR} and \algname{FedNL-LS}, which are variants of \algname{FedNL} that support partial participation, and globalization via cubic regularization and line search, respectively, and \algname{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 \algname{FedNL} methods have state-of-the-art communication complexity when compared to key baselines.

#### Author Information

##### Peter Richtarik (KAUST)

Peter Richtarik is an Associate Professor of Computer Science and Mathematics at KAUST and an Associate Professor of Mathematics at the University of Edinburgh. He is an EPSRC Fellow in Mathematical Sciences, Fellow of the Alan Turing Institute, and is affiliated with the Visual Computing Center and the Extreme Computing Research Center at KAUST. Dr. Richtarik received his PhD from Cornell University in 2007, and then worked as a Postdoctoral Fellow in Louvain, Belgium, before joining Edinburgh in 2009, and KAUST in 2017. Dr. Richtarik's research interests lie at the intersection of mathematics, computer science, machine learning, optimization, numerical linear algebra, high performance computing and applied probability. Through his recent work on randomized decomposition algorithms (such as randomized coordinate descent methods, stochastic gradient descent methods and their numerous extensions, improvements and variants), he has contributed to the foundations of the emerging field of big data optimization, randomized numerical linear algebra, and stochastic methods for empirical risk minimization. Several of his papers attracted international awards, including the SIAM SIGEST Best Paper Award, the IMA Leslie Fox Prize (2nd prize, twice), and the INFORMS Computing Society Best Student Paper Award (sole runner up). He is the founder and organizer of the Optimization and Big Data workshop series.​