On Convergence-Diagnostic based Step Sizes for Stochastic Gradient Descent

Scott Pesme (1) , Aymeric Dieuleveut (2) , Nicolas Flammarion (1)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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-word datasets.

Domaines: Statistiques [math.ST]; Apprentissage [cs.LG]

Scott Pesme, Aymeric Dieuleveut, Nicolas Flammarion. On Convergence-Diagnostic based Step Sizes for Stochastic Gradient Descent. 37th International Conference on Machine Learning (ICML 2020), Jul 2020, Vienne (en ligne), Austria. pp.119:7641-7651. ⟨hal-04554421⟩