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The fluctuation effect of gradient expectation and variance caused byparameter update between consecutive iterations is neglected or confusing bycurrent mainstream gradient optimization algorithms.Using this fluctuationeffect, combined with the stratified sampling strategy, this paper designs anovel \underline{M}emory \underline{S}tochastic s\underline{T}ratified GradientDescend(\underline{MST}GD) algorithm with an exponential convergence rate.Specifically, MSTGD uses two strategies for variance reduction: the firststrategy is to perform variance reduction according to the proportion p of usedhistorical gradient, which is estimated from the mean and variance of samplegradients before and after iteration, and the other strategy is stratifiedsampling by category. The statistic \ $\bar{G}_{mst}$\ designed under these twostrategies can be adaptively unbiased, and its variance decays at a geometricrate. This enables MSTGD based on $\bar{G}_{mst}$ to obtain an exponentialconvergence rate of the form $\lambda^{2(k-k_0)}$($\lambda\in (0,1)$,k is thenumber of iteration steps,$\lambda$ is a variable related to proportionp).Unlike most other algorithms that claim to achieve an exponentialconvergence rate, the convergence rate is independent of parameters such asdataset size N, batch size n, etc., and can be achieved at a constant stepsize.Theoretical and experimental results show the effectiveness of MSTGD

MSTGD:A Memory Stochastic sTratified Gradient Descent Method with an Exponential Convergence Rate