1. Federated Empirical Risk Minimization via Second-Order Method
- Author
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Bian, Song, Song, Zhao, and Yin, Junze
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Computer Science - Distributed, Parallel, and Cluster Computing ,Distributed, Parallel, and Cluster Computing (cs.DC) ,Machine Learning (cs.LG) - Abstract
Many convex optimization problems with important applications in machine learning are formulated as empirical risk minimization (ERM). There are several examples: linear and logistic regression, LASSO, kernel regression, quantile regression, $p$-norm regression, support vector machines (SVM), and mean-field variational inference. To improve data privacy, federated learning is proposed in machine learning as a framework for training deep learning models on the network edge without sharing data between participating nodes. In this work, we present an interior point method (IPM) to solve a general ERM problem under the federated learning setting. We show that the communication complexity of each iteration of our IPM is $\tilde{O}(d^{3/2})$, where $d$ is the dimension (i.e., number of features) of the dataset.
- Published
- 2023
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