Barzilai-Borwein Step Size for Stochastic Gradient Descent
This addresses the time-consuming manual tuning of step sizes in stochastic optimization for machine learning practitioners, though it is incremental as it adapts an existing method to SGD.
The paper tackles the problem of automatically selecting step sizes in stochastic gradient descent (SGD) and its variant SVRG by proposing the Barzilai-Borwein method, leading to algorithms SGD-BB and SVRG-BB that achieve performance comparable to or better than best-tuned step sizes in numerical experiments on standard datasets.
One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms, the common practice in SGD is either to use a diminishing step size, or to tune a fixed step size by hand, which can be time consuming in practice. In this paper, we propose to use the Barzilai-Borwein (BB) method to automatically compute step sizes for SGD and its variant: stochastic variance reduced gradient (SVRG) method, which leads to two algorithms: SGD-BB and SVRG-BB. We prove that SVRG-BB converges linearly for strongly convex objective functions. As a by-product, we prove the linear convergence result of SVRG with Option I proposed in [10], whose convergence result is missing in the literature. Numerical experiments on standard data sets show that the performance of SGD-BB and SVRG-BB is comparable to and sometimes even better than SGD and SVRG with best-tuned step sizes, and is superior to some advanced SGD variants.