ON THE EFFECT OF CONSENSUS IN DECENTRALIZED DEEP LEARNING Anonymous authors Paper under double-blind review

Abstract

Decentralized training of deep learning models enables on-device learning over networks, as well as efficient scaling to large compute clusters. Experiments in earlier works revealed that decentralized training often suffers from generalization issues: the performance of models trained in a decentralized fashion is in general worse than the performance of models trained in a centralized fashion, and this generalization gap is impacted by parameters such as network size, communication topology and data partitioning. We identify the changing consensus distance between devices as a key parameter to explain the gap between centralized and decentralized training. We show that when the consensus distance does not grow too large, the performance of centralized training can be reached and sometimes surpassed. We highlight the intimate interplay between network topology and learning rate at the different training phases and discuss the implications for communication efficient training schemes. Our insights into the generalization gap in decentralized deep learning allow the principled design of better training schemes that mitigate these effects.

1. INTRODUCTION

Highly over-parametrized deep neural networks show impressive results in machine learning tasks, which also lead to a dramatic increase in the size, complexity, and computational power of the training systems. In response to these challenges, distributed training algorithms (i.e. data-parallel large mini-batch SGD) have been developed for use in data-center (Goyal et al., 2017; You et al., 2018; Shallue et al., 2018) . These SOTA training systems in general use the All-Reduce communication primitive to perform exact averaging on the local mini-batch gradients computed on different subsets of the data, for the later synchronized model update. However, exact averaging with All-Reduce is sensitive to the communication hardware of the training systems, causing the bottleneck in efficient deep learning training. To this end, decentralized training has become an indispensable training paradigm for efficient large scale training in the data-center, alongside its orthogonal benefits on preserving users' privacy for edge AI (Bellet et al., 2018; Kairouz et al., 2019) . In this work, we theoretically identify the consensus distance, i.e. the average discrepancy between the nodes, as the key parameter that captures the joint effect of decentralization. We show that there exists a critical consensus distance: when the consensus distance is lower than this critical value, the optimization is almost unhindered. With the insight derived from optimization convergence,

