A Stochastic Newton Algorithm for Distributed Convex Optimization

Brian Bullins, Kumar Kshitij Patel, Ohad Shamir, Nathan Srebro, Blake Woodworth

Keywords: Distributed Optimization, Stochastic Optimization, Federated Learning, Newton's Method

TL;DR: We propose and analyze a stochastic Newton algorithm for homogeneous distributed convex optimization based on efficiently solving quadratic objectives in parallel with only a single round of communication.

Abstract: We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector products (products of an independent unbiased estimator of the Hessian of the population objective with arbitrary vectors), with many such stochastic computations performed between rounds of communication. We show that our method can reduce the number, and frequency, of required communication rounds, compared to existing methods without hurting performance, by proving convergence guarantees for quasi-self-concordant objectives (e.g., logistic regression), alongside empirical evidence.

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