In large-scale distributed computing clusters, such as Amazon EC2, there are several types of "system noise" that can result in major degradation of performance: system failures, bottlenecks due to limited communication bandwidth, latency due to straggler nodes, etc. On the other hand, these systems enjoy abundance of redundancy -a vast number of computing nodes and large storage capacity. There have been recent results that demonstrate the impact of coding for efficient utilization of computation and storage redundancy to alleviate the effect of stragglers and communication bottlenecks in homogeneous clusters. In this paper, we focus on general heterogeneous distributed computing clusters consisting of a variety of computing machines with different capabilities. We propose a coding framework for speeding up distributed computing in heterogeneous clusters by trading redundancy for reducing the latency of computation. In particular, we propose Heterogeneous Coded Matrix Multiplication (HCMM) algorithm for performing distributed matrix multiplication over heterogeneous clusters that is provably asymptotically optimal for a broad class of processing time distributions. Moreover, we show that HCMM is unboundedly faster than uncoded schemes that partition the total work load among the workers. To demonstrate how the proposed HCMM scheme can be applied in practice, we provide numerical results demonstrating significant speedups of up to 90% and 35% for HCMM in comparison to the "uncoded" and "coded homogeneous" schemes, respectively. Furthermore, we carry out real experiments over Amazon EC2 clusters that corroborate our numerical studies, where HCMM is found to be up to 17% faster than the uncoded scheme. Additionally, our observation is that machines rarely become stragglers and when they do, they continue to exhibit slower performance for sometime. In our worst case experiments with artificial stragglers, HCMM provides speedups of up to 12× over the uncoded scheme. Furthermore, we provide a generalization of the problem of optimal load allocation for heterogeneous clusters to scenarios with budget constraints and develop a heuristic algorithm for efficient load allocation. In the end, we discuss about the decoding complexity and describe how LDPC codes can be combined with HCMM in order to control the complexity of decoding as the problem size increases.
We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to 13.43×, and also achieves a 2.36×-12.65× speedup over the state-of-the-art straggler mitigation strategies.
Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.
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