AISTATS 2017poster14 citations
Sparse Accelerated Exponential Weights
Pierre Gaillard, Olivier Wintenberger
Abstract
We consider the stochastic optimization problem where a convex function is minimized observing recursively the gradients. We introduce SAEW, a new procedure that accelerates exponential weights procedures with the slow rate $1/\sqrtT$ to procedures achieving the fast rate $1/T$. Under the strong convexity of the risk, we achieve the optimal rate of convergence for approximating sparse parameters in $R^d$. The acceleration is achieved by using successive averaging steps in an online fashion. The procedure also produces sparse estimators thanks to additional hard threshold steps.
BibTeX
@InProceedings{pmlr-v54-gaillard17a,
title = {{Sparse Accelerated Exponential Weights}},
author = {Gaillard, Pierre and Wintenberger, Olivier},
booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {75--82},
year = {2017},
editor = {Singh, Aarti and Zhu, Jerry},
volume = {54},
series = {Proceedings of Machine Learning Research},
month = {20--22 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v54/gaillard17a/gaillard17a.pdf},
url = {https://proceedings.mlr.press/v54/gaillard17a.html},
abstract = {We consider the stochastic optimization problem where a convex function is minimized observing recursively the gradients. We introduce SAEW, a new procedure that accelerates exponential weights procedures with the slow rate $1/\sqrtT$ to procedures achieving the fast rate $1/T$. Under the strong convexity of the risk, we achieve the optimal rate of convergence for approximating sparse parameters in $R^d$. The acceleration is achieved by using successive averaging steps in an online fashion. The procedure also produces sparse estimators thanks to additional hard threshold steps. }
}