In order to better cope with large-scale high-dimensional sparse data sets in today's era, this paper combined the advantages of BB method, mini-batch algorithm and stochastic variance reduced gradient(SVRG), and proposed a mini-batch sparse stochastic variance reduced gradient method(MSSVRG-R2BB) with randomly improved Barzilai-Borwein step size. Firstly, on the basis of calculating the total gradient in the outer loop of SVRG, this paper added the subgradient of L₁ norm, designed a sparse approximate gradient for the inner loop of SVRG, and obtained a sparse SVRG algorithm(SSVRG). On this basis, it proposed to use the improved BB method of random selection to automatically calculate and update the step size in the mini-batch sparse stochastic variance reduced gradient method, which solved the step size selection problem of the mini-batch algorithm, and expanded the MSSVRG-R2BB algorithm. Numerical experiments show that MSSVRG-R2BB algorithm can not only reduce the operation cost and reach the convergence upper bound faster, but also achieve the same optimization level of other advanced small-batch algorithms, and perform stably and well for different initial parameter selection.

[2023-07-13] Accepted Paper /doc/2023.04.0177/v1

[2023-12-05] Printed Article /doc/2023.04.0177/v2