Delay-tolerant distributed Bregman proximal algorithms

TL;DR

This paper introduces a delay-tolerant asynchronous distributed Bregman proximal-gradient algorithm that effectively handles long delays in distributed systems, improving optimization for non-Lipschitz continuous gradient problems like Poisson inverse problems.

Contribution

It proposes a novel asynchronous distributed Bregman proximal-gradient method that is robust to delays and adaptable to various centralized computing architectures.

Findings

Algorithm copes with arbitrarily long delays.

Effective for distributed Poisson inverse problems.

Enhances optimization when gradients are not Lipschitz continuous.

Abstract

Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which compromises the use of (proximal) gradient algorithms. Fortunately, changing the geometry and using Bregman divergences can alleviate this issue in several applications, such as for Poisson linear inverse problems.However, the Bregman operation makes the aggregation of several points and gradients more involved, hindering the distribution of computations for such problems. In this paper, we propose an asynchronous variant of the Bregman proximal-gradient method, able to adapt to any centralized computing system. In particular, we prove that the algorithm copes with arbitrarily long delays and we illustrate its behavior on distributed Poisson inverse problems.