Scale up with Order: Finding Good Data Permutations for Distributed Training

Gradient Balancing (GraB) is a recently proposed technique that finds provably better data permutations when training models with multiple epochs over a finite dataset. It converges at a faster rate than the widely adopted Random Reshuffling, by minimizing the discrepancy of the gradients on adjacently selected examples. However, GraB only operates under critical assumptions such as small batch sizes and centralized data, leaving open the question of how to order examples at large scale -- i.e. distributed learning with decentralized data. To alleviate the limitation, in this paper we propose D-GraB, an algorithm that orders the examples in a parallel setting with negligible overhead, which enjoys linear speed up at rate $\tilde{O}((mnT)^{-2/3})$ on smooth non-convex objectives and $\tilde{O}((mnT)^{-2})$ under PL condition, where $n$ denotes the number of parallel workers, $m$ denotes the number of examples per worker and $T$ denotes the number of epochs. D-GraB benefits from both data ordering and parallelism. Empirically, we show on various applications including GLUE, CIFAR10 and WikiText-2 that D-GraB outperforms naive parallel GraB and Distributed Random Reshuffling in terms of both training and validation performance.