SVRG and SARAH converge with a weighted averaging scheme driven by estimate sequences, and when combined with Barzilai-Borwein step sizes and an adaptive inner-loop rule they become almost tune-free in numerical tests.
In order to prove Theorem 2, we need to borrow the following result from [Nguyen et al., 2017]
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Almost Tune-Free Variance Reduction
SVRG and SARAH converge with a weighted averaging scheme driven by estimate sequences, and when combined with Barzilai-Borwein step sizes and an adaptive inner-loop rule they become almost tune-free in numerical tests.