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Large-scale optimization problems require algorithms both effective andefficient. One such popular and proven algorithm is Stochastic Gradient Descentwhich uses first-order gradient information to solve these problems. This paperstudies almost-sure convergence rates of the Stochastic Gradient Descent methodwhen instead of deterministic, its learning rate becomes stochastic. Inparticular, its learning rate is equipped with a multiplicative stochasticity,producing a stochastic learning rate scheme. Theoretical results showaccelerated almost-sure convergence rates of Stochastic Gradient Descent in anonconvex setting when using an appropriate stochastic learning rate, comparedto a deterministic-learning-rate scheme. The theoretical results are verifiedempirically.

Accelerated Almost-Sure Convergence Rates for Nonconvex Stochastic Gradient Descent using Stochastic Learning Rates