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Sparsified SGD with Memory
Sebastian Stich · Jean-Baptiste Cordonnier · Martin Jaggi

Wed Dec 05 07:45 AM -- 09:45 AM (PST) @ Room 210 #10

Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders perfect scalability. Various recent works proposed to use quantization or sparsification techniques to reduce the amount of data that needs to be communicated, for instance by only sending the most significant entries of the stochastic gradient (top-k sparsification). Whilst such schemes showed very promising performance in practice, they have eluded theoretical analysis so far.

In this work we analyze Stochastic Gradient Descent (SGD) with k-sparsification or compression (for instance top-k or random-k) and show that this scheme converges at the same rate as vanilla SGD when equipped with error compensation (keeping track of accumulated errors in memory). That is, communication can be reduced by a factor of the dimension of the problem (sometimes even more) whilst still converging at the same rate. We present numerical experiments to illustrate the theoretical findings and the good scalability for distributed applications.

Author Information

Sebastian Stich (EPFL)

Dr. [Sebastian U. Stich](https://sstich.ch/) is a postdoctoral researcher in machine learning at EPFL (Lausanne, Switzerland). Research interests: - *methods for machine learning and statistics*—at the interface of theory and practice - *collaborative learning* (distributed, federated and decentralized methods) - *optimization for machine learning* (adaptive stochastic methods and generalization performance)

Jean-Baptiste Cordonnier (EPFL)
Martin Jaggi (EPFL)

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