Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been observed that the speedup saturates beyond a certain batch size and/or when the delays grow too large. We identify a data-dependent parameter that explains the speedup saturation in both these settings. Our comprehensive theoretical analysis, for strongly convex, convex and non-convex settings, unifies and generalized prior work directions that often focused on only one of these two aspects. In particular, our approach allows us to derive improved speedup results under frequently considered sparsity assumptions. Our insights give rise to theoretically based guidelines on how the learning rates can be adjusted in practice. We show that our results are tight and illustrate key findings in numerical experiments.

Consensus Control for Decentralized Deep Learning

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 reveal that, even in a data-center setup, decentralized training often suffers from the degradation in the quality of the model: the training and test performance of models trained in a decentralized fashion is in general worse than that of models trained in a centralized fashion, and this performance drop 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 in theory that when the training consensus distance is lower than a critical quantity, decentralized training converges as fast as the centralized counterpart. We empirically validate that the relation between generalization performance and consensus distance is consistent with this theoretical observation. Our empirical insights allow the principled design of better decentralized training schemes that mitigate the performance drop. To this end, we propose practical training guidelines for the data-center setup as the important first step.

Quasi-Global Momentum: Accelerating Decentralized Deep Learning on Heterogeneous Data

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an optimization challenge and may severely deteriorate the generalization performance. In this paper, we investigate and identify the limitation of several decentralized optimization algorithms for different degrees of data heterogeneity. We propose a novel momentum-based method to mitigate this decentralized training difficulty. We show in extensive empirical experiments on various CV/NLP datasets (CIFAR-10, ImageNet, AG News, and SST2) and several network topologies (Ring and Social Network) that our method is much more robust to the heterogeneity of clients' data than other existing methods, by a significant improvement in test performance ($1\% \!-\! 20\%$).

Exact Optimization of Conformal Predictors via Incremental and Decremental Learning

Conformal Predictors (CP) are wrappers around ML methods, providing error guarantees under weak assumptions on the data distribution. They are suitable for a wide range of problems, from classification and regression to anomaly detection. Unfortunately, their high computational complexity limits their applicability to large datasets. In this work, we show that it is possible to speed up a CP classifier considerably, by studying it in conjunction with the underlying ML method, and by exploiting incremental&decremental learning. For methods such as k-NN, KDE, and kernel LS-SVM, our approach reduces the running time by one order of magnitude, whilst producing exact solutions. With similar ideas, we also achieve a linear speed up for the harder case of bootstrapping. Finally, we extend these techniques to improve upon an optimization of k-NN CP for regression. We evaluate our findings empirically, and discuss when methods are suitable for CP optimization.

Learning from History for Byzantine Robust Optimization

Byzantine robustness has received significant attention recently given its importance for distributed and federated learning. In spite of this, we identify severe flaws in existing algorithms even when the data across the participants is assumed to be identical. First, we show that most existing robust aggregation rules may not converge even in the absence of any Byzantine attackers, because they are overly sensitive to the distribution of the noise in the stochastic gradients. Secondly, we show that even if the aggregation rules may succeed in limiting the influence of the attackers in a single round, the attackers can couple their attacks across time eventually leading to divergence. To address these issues, we present two surprisingly simple strategies: a new iterative clipping procedure, and incorporating worker momentum to overcome time-coupled attacks. This is the first provably robust method for the standard stochastic non-convex optimization setting.

A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!

Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain the first scheme that converges linearly on strongly convex decentralized problems while using compressed communication only. We prove that our method can solve the problems without any increase in the number of communications compared to the baseline which does not perform any communication compression while still allowing for a significant compression factor which depends on the conditioning of the problem and the topology of the network. Our key theoretical findings are supported by numerical experiments.

Sparse Communication for Training Deep Networks

Synchronous stochastic gradient descent (SGD) is the most common method used for distributed training of deep learning models. In this algorithm, each worker shares its local gradients with others and updates the parameters using the average gradients of all workers. Although distributed training reduces the computation time, the communication overhead associated with the gradient exchange forms a scalability bottleneck for the algorithm. There are many compression techniques proposed to reduce the number of gradients that needs to be communicated. However, compressing the gradients introduces yet another overhead to the problem. In this work, we study several compression schemes and identify how three key parameters affect the performance. We also provide a set of insights on how to increase performance and introduce a simple sparsification scheme, random-block sparsification, that reduces communication while keeping the performance close to standard SGD.

Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning

Federated learning is a challenging optimization problem due to the heterogeneity of the data across different clients. Such heterogeneity has been observed to induce client drift and significantly degrade the performance of algorithms designed for this setting. In contrast, centralized learning with centrally collected data does not experience such drift, and has seen great empirical and theoretical progress with innovations such as momentum, adaptivity, etc. In this work, we propose a general framework Mime which mitigates client-drift and adapts arbitrary centralized optimization algorithms (e.g.\ SGD, Adam, etc.) to federated learning. Mime uses a combination of control-variates and server-level statistics (e.g. momentum) at every client-update step to ensure that each local update mimics that of the centralized method. Our thorough theoretical and empirical analyses strongly establish Mime's superiority over other baselines.

PowerGossip: Practical Low-Rank Communication Compression in Decentralized Deep Learning

Lossy gradient compression has become a practical tool to overcome the communication bottleneck in centrally coordinated distributed training of machine learning models. However, algorithms for decentralized training with compressed communication over arbitrary connected networks have been more complicated, requiring additional memory and hyperparameters. We introduce a simple algorithm that directly compresses the model differences between neighboring workers using low-rank linear compressors applied on model differences. Inspired by the PowerSGD algorithm for centralized deep learning, this algorithm uses power iteration steps to maximize the information transferred per bit. We prove that our method requires no additional hyperparameters, converges faster than prior methods, and is asymptotically independent of both the network and the compression. Out of the box, these compressors perform on par with state-of-the-art tuned compression algorithms in a series of deep learning benchmarks.

Multi-Head Attention: Collaborate Instead of Concatenate

Attention layers are widely used in natural language processing (NLP) and are beginning to influence computer vision architectures. However, they suffer from over-parameterization. For instance, it was shown that the majority of attention heads could be pruned without impacting accuracy. This work aims to enhance current understanding on how multiple heads interact. Motivated by the observation that trained attention heads share common key/query projections, we propose a collaborative multi-head attention layer that enables heads to learn shared projections. Our scheme improves the computational cost and number of parameters in an attention layer and can be used as a drop-in replacement in any transformer architecture. For instance, by allowing heads to collaborate on a neural machine translation task, we can reduce the key dimension by a factor of eight without any loss in performance. We also show that it is possible to re-parametrize a pre-trained multi-head attention layer into our collaborative attention layer. Even without retraining, collaborative multi-head attention manages to reduce the size of the key and query projections by half without sacrificing accuracy. Our code is public.