Jul 12, 2020

We investigate the generalisation performance of Distributed Gradient Descent with implicit regularisation and random features in the homogenous setting where a network of agents are given data sampled independently from the same unknown distribution. Along with reducing the memory footprint, random features are particularly convenient in this setting as they provide a common parameterisation across agents that allows to overcome previous difficulties in implementing decentralised kernel regression. Under standard source and capacity assumptions, we establish high probability bounds on the predictive performance for each agent as a function of the step size, number of iterations, inverse spectral gap of the communication matrix and number of random features. By tuning these parameters, we obtain statistical rates that are minimax optimal with respect to the total number of samples in the network. The algorithm provides a linear improvement over single-machine gradient descent in memory cost and, when agents hold enough data with respect to the network size and inverse spectral gap, a linear speed up in computational run-time for any network topology. We present simulations that show how the number of random features, iterations and samples impact predictive performance.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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