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Register a new userCommunication-Efficient Gradient Coding for Straggler Mitigation in Distributed Learning
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Swanand Kadhe
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Distributed implementations of gradient-based methods, wherein a server distributes gradient computations across worker machines, need to overcome two limitations: delays caused by slow running machines called stragglers, and communication overheads. Recently, Ye and Abbe [ICML 2018] proposed a coding-theoretic paradigm to characterize a fundamental trade-off between computation load per worker, communication overhead per worker, and straggler tolerance. However, their proposed coding schemes suffer from heavy decoding complexity and poor numerical stability. In this paper, we develop a communication-efficient gradient coding framework to overcome these drawbacks. Our proposed framework enables using any linear code to design the encoding and decoding functions. When a particular code is used in this framework, its block-length determines the computation load, dimension determines the communication overhead, and minimum distance determines the straggler tolerance. The flexibility of choosing a code allows us to gracefully trade-off the straggler threshold and communication overhead for smaller decoding complexity and higher numerical stability. Further, we show that using a maximum distance separable (MDS) code generated by a random Gaussian matrix in our framework yields a gradient code that is optimal with respect to the trade-off and, in addition, satisfies stronger guarantees on numerical stability as compared to the previously proposed schemes. Finally, we evaluate our proposed framework on Amazon EC2 and demonstrate that it reduces the average iteration time by 16% as compared to prior gradient coding schemes.
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In distributed synchronous gradient descent (GD) the main performance bottleneck for the per-iteration completion time is the slowest textit{straggling} workers. To speed up GD iterations in the presence of stragglers, coded distributed computation techniques are implemented by assigning redundant computations to workers. In this paper, we propose a novel gradient coding (GC) scheme that utilizes dynamic clustering, denoted by GC-DC, to speed up the gradient calculation. Under time-correlated straggling behavior, GC-DC aims at regulating the number of straggling workers in each cluster based on the straggler behavior in the previous iteration. We numerically show that GC-DC provides significant improvements in the average completion time (of each iteration) with no increase in the communication load compared to the original GC scheme.
Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A significant performance bottleneck for the per-iteration completion time in distributed synchronous GD is $straggling$ workers. Coded distributed computation techniques have been introduced recently to mitigate stragglers and to speed up GD iterations by assigning redundant computations to workers. In this paper, we consider gradient coding (GC), and propose a novel dynamic GC scheme, which assigns redundant data to workers to acquire the flexibility to dynamically choose from among a set of possible codes depending on the past straggling behavior. In particular, we consider GC with clustering, and regulate the number of stragglers in each cluster by dynamically forming the clusters at each iteration; hence, the proposed scheme is called $GC$ $with$ $dynamic$ $clustering$ (GC-DC). Under a time-correlated straggling behavior, GC-DC gains from adapting to the straggling behavior over time such that, at each iteration, GC-DC aims at distributing the stragglers across clusters as uniformly as possible based on the past straggler behavior. For both homogeneous and heterogeneous worker models, we numerically show that GC-DC provides significant improvements in the average per-iteration completion time without an increase in the communication load compared to the original GC scheme.
Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for computation at the agents is affected by the availability of local resources giving rise to the straggler problem in which the computation results are held back by unresponsive agents. For this problem, linear coding of the matrix sub-blocks can be used to introduce resilience toward straggling. The Parameter Server (PS) utilizes a channel code and distributes the matrices to the workers for multiplication. It then produces an approximation to the desired matrix multiplication using the results of the computations received at a given deadline. In this paper, we propose to employ Unequal Error Protection (UEP) codes to alleviate the straggler problem. The resiliency level of each sub-block is chosen according to its norm as blocks with larger norms have higher effects on the result of the matrix multiplication. We validate the effectiveness of our scheme both theoretically and through numerical evaluations. We derive a theoretical characterization of the performance of UEP using random linear codes, and compare it the case of equal error protection. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN), for which we investigate the fundamental trade-off between precision and the time required for the computations.
Master-worker distributed computing systems use task replication in order to mitigate the effect of slow workers, known as stragglers. Tasks are grouped into batches and assigned to one or more workers for execution. We first consider the case when the batches do not overlap and, using the results from majorization theory, show that, for a general class of workers service time distributions, a balanced assignment of batches to workers minimizes the average job compute time. We next show that this balanced assignment of non-overlapping batches achieves lower average job compute time compared to the overlapping schemes proposed in the literature. Furthermore, we derive the optimum redundancy level as a function of the service time distribution at workers. We show that the redundancy level that minimizes average job compute time is not necessarily the same as the redundancy level that maximizes the predictability of job compute time, and thus there exists a trade-off between optimizing the two metrics. Finally, by running experiments on Google cluster traces, we observe that redundancy can reduce the compute time of the jobs in Google clusters by an order of magnitude, and that the optimum level of redundancy depends on the distribution of tasks service time.
We propose a novel distributed iterative linear inverse solver method. Our method, PolyLin, has significantly lower communication cost, both in terms of number of rounds as well as number of bits, in comparison with the state of the art at the cost of higher computational complexity and storage. Our algorithm also has a built-in resilience to straggling and faulty computation nodes. We develop a natural variant of our main algorithm that trades off communication cost for computational complexity. Our method is inspired by ideas in error correcting codes.
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