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In this work, multiplicative stochasticity is applied to the learning rate ofstochastic optimization algorithms, giving rise to stochastic learning-rateschemes. In-expectation theoretical convergence results of Stochastic GradientDescent equipped with this novel stochastic learning rate scheme under thestochastic setting, as well as convergence results under the onlineoptimization settings are provided. Empirical results consider the case of anadaptively uniformly distributed multiplicative stochasticity and include notonly Stochastic Gradient Descent, but also other popular algorithms equippedwith a stochastic learning rate. They demonstrate noticeable optimizationperformance gains, with respect to their deterministic-learning-rate versions.

Stochastic Learning Rate Optimization in the Stochastic Approximation and Online Learning Settings