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Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this paper, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ā2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ā2 -subspace embedding, and that our resulting approximation converges to the optimal solution.
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Weighted Gradient Coding with Leverage Score Sampling
A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. Leverage score sampling provides a compressed approximation of a data matrix using an importance weighted subset. Gradient coding has been recently proposed in distributed optimization to compute the gradient using multiple unreliable worker nodes. By designing coding matrices, gradient coded computations can be made resilient to stragglers, which are nodes in a distributed network that degrade system performance. We present a novel weighted leverage score approach, that achieves improved performance for distributed gradient coding by utilizing an importance sampling.
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- Award ID(s):
- 1838179
- PAR ID:
- 10206905
- Date Published:
- Journal Name:
- International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2020
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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