Statistically Preconditioned Accelerated Gradient Method for Distributed Optimization

02/25/2020
by   Hadrien Hendrikx, et al.
0

We consider the setting of distributed empirical risk minimization where multiple machines compute the gradients in parallel and a centralized server updates the model parameters. In order to reduce the number of communications required to reach a given accuracy, we propose a preconditioned accelerated gradient method where the preconditioning is done by solving a local optimization problem over a subsampled dataset at the server. The convergence rate of the method depends on the square root of the relative condition number between the global and local loss functions. We estimate the relative condition number for linear prediction models by studying uniform concentration of the Hessians over a bounded domain, which allows us to derive improved convergence rates for existing preconditioned gradient methods and our accelerated method. Experiments on real-world datasets illustrate the benefits of acceleration in the ill-conditioned regime.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/07/2022

Nesterov Accelerated Shuffling Gradient Method for Convex Optimization

In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG)...
03/13/2020

Iterative Pre-Conditioning to Expedite the Gradient-Descent Method

Gradient-descent method is one of the most widely used and perhaps the m...
02/26/2020

Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization

Due to the high communication cost in distributed and federated learning...
07/20/2021

CANITA: Faster Rates for Distributed Convex Optimization with Communication Compression

Due to the high communication cost in distributed and federated learning...
02/28/2018

Parametrized Accelerated Methods Free of Condition Number

Analyses of accelerated (momentum-based) gradient descent usually assume...
11/12/2020

Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration

We show that standard extragradient methods (i.e. mirror prox and dual e...
03/11/2020

Majorization Minimization Methods to Distributed Pose Graph Optimization with Convergence Guarantees

In this paper, we consider the problem of distributed pose graph optimiz...