Arjun Rajkumar

Tahseen Rabbani, Brandon Feng, Marco Bornstein et al.

Federated learning (FL) is a popular paradigm for private and collaborative model training on the edge. In centralized FL, the parameters of a global architecture (such as a deep neural network) are maintained and distributed by a central server/controller to clients who transmit model updates (gradients) back to the server based on local optimization. While many efforts have focused on reducing the communication complexity of gradient transmission, the vast majority of compression-based algorithms assume that each participating client is able to download and train the current and full set of parameters, which may not be a practical assumption depending on the resource constraints of smaller clients such as mobile devices. In this work, we propose a simple yet effective novel algorithm, Comfetch, which allows clients to train large networks using reduced representations of the global architecture via the count sketch, which reduces local computational and memory costs along with bi-directional communication complexity. We provide a nonconvex convergence guarantee and experimentally demonstrate that it is possible to learn large models, such as a deep convolutional network, through federated training on their sketched counterparts. The resulting global models exhibit competitive test accuracy over CIFAR10/100 classification when compared against un-compressed model training.

Tahseen Rabbani, Apollo Jain, Arjun Rajkumar et al.

The power method is a classical algorithm with broad applications in machine learning tasks, including streaming PCA, spectral clustering, and low-rank matrix approximation. The distilled purpose of the vanilla power method is to determine the largest eigenvalue (in absolute modulus) and its eigenvector of a matrix. A momentum-based scheme can be used to accelerate the power method, but achieving an optimal convergence rate with existing algorithms critically relies on additional spectral information that is unavailable at run-time, and sub-optimal initializations can result in divergence. In this paper, we provide a pair of novel momentum-based power methods, which we call the delayed momentum power method (DMPower) and a streaming variant, the delayed momentum streaming method (DMStream). Our methods leverage inexact deflation and are capable of achieving near-optimal convergence with far less restrictive hyperparameter requirements. We provide convergence analyses for both algorithms through the lens of perturbation theory. Further, we experimentally demonstrate that DMPower routinely outperforms the vanilla power method and that both algorithms match the convergence speed of an oracle running existing accelerated methods with perfect spectral knowledge.