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Variable metric proximal gradient methods with different metric selectionshave been widely used in composite optimization. Combining the Barzilai-Borwein(BB) method with a diagonal selection strategy for the metric, the diagonal BBstepsize can keep low per-step computation cost as the scalar BB stepsize andbetter capture the local geometry of the problem. In this paper, we propose avariable metric mini-batch proximal stochastic recursive gradient algorithmVM-mSRGBB, which updates the metric using a new diagonal BB stepsize. Thelinear convergence of VM-mSRGBB is established for strongly convex,non-strongly convex and convex functions. Numerical experiments on standarddata sets show that VM-mSRGBB is better than or comparable to some variancereduced stochastic gradient methods with best-tuned scalar stepsizes or BBstepsizes. Furthermore, the performance of VM-mSRGBB is superior to someadvanced mini-batch proximal stochastic gradient methods.

A variable metric mini-batch proximal stochastic recursive gradient algorithm with diagonal Barzilai-Borwein stepsize