ICML 2019oral7 citations
Characterization of Convex Objective Functions and Optimal Expected Convergence Rates for SGD
Marten Van Dijk, Lam Nguyen, Phuong Ha Nguyen, Dzung Phan
Abstract
We study Stochastic Gradient Descent (SGD) with diminishing step sizes for convex objective functions. We introduce a definitional framework and theory that defines and characterizes a core property, called curvature, of convex objective functions. In terms of curvature we can derive a new inequality that can be used to compute an optimal sequence of diminishing step sizes by solving a differential equation. Our exact solutions confirm known results in literature and allows us to fully characterize a new regularizer with its corresponding expected convergence rates.
BibTeX
@InProceedings{pmlr-v97-van-dijk19a,
title = {Characterization of Convex Objective Functions and Optimal Expected Convergence Rates for {SGD}},
author = {Van Dijk, Marten and Nguyen, Lam and Nguyen, Phuong Ha and Phan, Dzung},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {6392--6400},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/van-dijk19a/van-dijk19a.pdf},
url = {https://proceedings.mlr.press/v97/van-dijk19a.html},
abstract = {We study Stochastic Gradient Descent (SGD) with diminishing step sizes for convex objective functions. We introduce a definitional framework and theory that defines and characterizes a core property, called curvature, of convex objective functions. In terms of curvature we can derive a new inequality that can be used to compute an optimal sequence of diminishing step sizes by solving a differential equation. Our exact solutions confirm known results in literature and allows us to fully characterize a new regularizer with its corresponding expected convergence rates.}
}