Making Asynchronous Stochastic Gradient Descent Work for Transformers

Asynchronous stochastic gradient descent (SGD) is attractive from a speed perspective because workers do not wait for synchronization. However, the Transformer model converges poorly with asynchronous SGD, resulting in substantially lower quality compared to synchronous SGD. To investigate why this is the case, we isolate differences between asynchronous and synchronous methods to investigate batch size and staleness effects. We find that summing several asynchronous updates, rather than applying them immediately, restores convergence behavior. With this hybrid method, Transformer training for neural machine translation task reaches a near-convergence level 1.36x faster in single-node multi-GPU training with no impact on model quality

A Coordinate-Descent Algorithm for Tracking Solutions in Time-Varying Optimal Power Flows

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of transmission-constrained problems in power systems. On the example of the alternating-current optimal power flows (ACOPF), we bound the difference between the current approximate optimal cost generated by our algorithm and the optimal cost for a relaxation using the most recent data from above by a function of the properties of the instance and the rate of change to the instance over time. We also bound the number of floating-point operations that need to be performed between two updates in order to guarantee the error is bounded from above by a given constant

Newton-Raphson Consensus for Distributed Convex Optimization

We address the problem of distributed uncon- strained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton- Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.Comment: 18 pages, preprint with proof

Taming Unbalanced Training Workloads in Deep Learning with Partial Collective Operations

Load imbalance pervasively exists in distributed deep learning training systems, either caused by the inherent imbalance in learned tasks or by the system itself. Traditional synchronous Stochastic Gradient Descent (SGD) achieves good accuracy for a wide variety of tasks, but relies on global synchronization to accumulate the gradients at every training step. In this paper, we propose eager-SGD, which relaxes the global synchronization for decentralized accumulation. To implement eager-SGD, we propose to use two partial collectives: solo and majority. With solo allreduce, the faster processes contribute their gradients eagerly without waiting for the slower processes, whereas with majority allreduce, at least half of the participants must contribute gradients before continuing, all without using a central parameter server. We theoretically prove the convergence of the algorithms and describe the partial collectives in detail. Experimental results on load-imbalanced environments (CIFAR-10, ImageNet, and UCF101 datasets) show that eager-SGD achieves 1.27x speedup over the state-of-the-art synchronous SGD, without losing accuracy.Comment: Published in Proceedings of the 25th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP'20), pp. 45-61. 202

SWARM Parallelism: Training Large Models Can Be Surprisingly Communication-Efficient

Many deep learning applications benefit from using large models with billions of parameters. Training these models is notoriously expensive due to the need for specialized HPC clusters. In this work, we consider alternative setups for training large models: using cheap "preemptible" instances or pooling existing resources from multiple regions. We analyze the performance of existing model-parallel algorithms in these conditions and find configurations where training larger models becomes less communication-intensive. Based on these findings, we propose SWARM parallelism, a model-parallel training algorithm designed for poorly connected, heterogeneous and unreliable devices. SWARM creates temporary randomized pipelines between nodes that are rebalanced in case of failure. We empirically validate our findings and compare SWARM parallelism with existing large-scale training approaches. Finally, we combine our insights with compression strategies to train a large Transformer language model with 1B shared parameters (approximately 13B before sharing) on preemptible T4 GPUs with less than 200Mb/s network.Comment: Accepted to International Conference on Machine Learning (ICML) 2023. 25 pages, 8 figure

Breaking (Global) Barriers in Parallel Stochastic Optimization with Wait-Avoiding Group Averaging

Deep learning at scale is dominated by communication time. Distributing samples across nodes usually yields the best performance, but poses scaling challenges due to global information dissemination and load imbalance across uneven sample lengths. State-of-the-art decentralized optimizers mitigate the problem, but require more iterations to achieve the same accuracy as their globally-communicating counterparts. We present Wait-Avoiding Group Model Averaging (WAGMA) SGD, a wait-avoiding stochastic optimizer that reduces global communication via subgroup weight exchange. The key insight is a combination of algorithmic changes to the averaging scheme and the use of a group allreduce operation. We prove the convergence of WAGMA-SGD, and empirically show that it retains convergence rates similar to Allreduce-SGD. For evaluation, we train ResNet-50 on ImageNet; Transformer for machine translation; and deep reinforcement learning for navigation at scale. Compared with state-of-the-art decentralized SGD variants, WAGMA-SGD significantly improves training throughput (e.g., 2.1x on 1,024 GPUs for reinforcement learning), and achieves the fastest time-to-solution (e.g., the highest score using the shortest training time for Transformer).Comment: Published in IEEE Transactions on Parallel and Distributed Systems (IEEE TPDS), vol. 32, no. 7, pp. 1725-1739, 1 July 202