Year: 2020
Type: preprint
Abstract: Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In this paper, we show that efficiently detecting this transition and appropriately decreasing the step size can lead to fast convergence rates. We analyse the classical statistical test proposed by Pflug (1983), based on the inner product between consecutive stochastic gradients. Even in the simple case where the objective function is quadratic we show that this test cannot lead to an adequate convergence diagnostic. We then propose a novel and simple statistical procedure that accurately detects stationarity and we provide experimental results showing state-of-the-art performance on synthetic and real-world datasets.
Source: arXiv (Cornell University)
Institutions: École Polytechnique Fédérale de Lausanne, École Polytechnique
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3034900235