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Data-Dependent Convergence for Consensus Stochastic Optimization
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DOI：10.1109/TAC.2017.2671377.png)
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Abstract
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We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: The standard spectral gap of a weight matrix from the network topology and a new term depending on the spectral norm of the sample covariance matrix of the data. This data-dependent convergence rate shows that distributed SGD algorithms perform better on datasets with small spectral norm. Our analysis method also allows us to find data-dependent convergence rates as we limit the amount of communication. Spreading a fixed amount of data across more nodes slows convergence; for asymptotically growing datasets, we show that addingmoremachines can help when minimizing twice-differentiable losses.
Keywords:
Convergence
distributed computing
machine learning
minimization
optimization
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