On Consensus-Optimality Trade-offs in Collaborative Deep Learning

TL;DR

This paper introduces new distributed deep learning algorithms that balance consensus and optimality, providing theoretical convergence guarantees and demonstrating improved performance through experiments.

Contribution

The paper proposes the i-CDSGD and g-CDSGD algorithms, enabling flexible trade-offs between consensus and disagreement in distributed deep learning.

Findings

Algorithms converge for strongly convex and nonconvex objectives

Momentum variants improve convergence in strongly convex cases

Numerical experiments show significant performance improvements

Abstract

In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality. In this paper, we build on recent algorithmic progresses in distributed deep learning to explore various consensus-optimality trade-offs over a fixed communication topology. First, we propose the incremental consensus-based distributed SGD (i-CDSGD) algorithm, which involves multiple consensus steps (where each agent communicates information with its neighbors) within each SGD iteration. Second, we propose the generalized consensus-based distributed SGD (g-CDSGD) algorithm that enables us to navigate the full spectrum from complete consensus (all agents agree) to complete disagreement (each agent converges to individual model parameters). We analytically establish convergence of the proposed algorithms for strongly convex and nonconvex objective functions; we also analyze the momentum variants of the algorithms for the strongly convex case. We support our algorithms via numerical experiments, and demonstrate significant improvements over existing methods for collaborative deep learning.