ICML 2015poster40 citations
The Hedge Algorithm on a Continuum
Walid Krichene, Maximilian Balandat, Claire Tomlin, Alexandre Bayen
Abstract
We consider an online optimization problem on a subset S of R^n (not necessarily convex), in which a decision maker chooses, at each iteration t, a probability distribution x^(t) over S, and seeks to minimize a cumulative expected loss, where each loss is a Lipschitz function revealed at the end of iteration t. Building on previous work, we propose a generalized Hedge algorithm and show a O(\sqrtt \log t) bound on the regret when the losses are uniformly Lipschitz and S is uniformly fat (a weaker condition than convexity). Finally, we propose a generalization to the dual averaging method on the set of Lebesgue-continuous distributions over S.
BibTeX
@InProceedings{pmlr-v37-krichene15,
title = {The Hedge Algorithm on a Continuum},
author = {Krichene, Walid and Balandat, Maximilian and Tomlin, Claire and Bayen, Alexandre},
booktitle = {Proceedings of the 32nd International Conference on Machine Learning},
pages = {824--832},
year = {2015},
editor = {Bach, Francis and Blei, David},
volume = {37},
series = {Proceedings of Machine Learning Research},
address = {Lille, France},
month = {07--09 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v37/krichene15.pdf},
url = {https://proceedings.mlr.press/v37/krichene15.html},
abstract = {We consider an online optimization problem on a subset S of R^n (not necessarily convex), in which a decision maker chooses, at each iteration t, a probability distribution x^(t) over S, and seeks to minimize a cumulative expected loss, where each loss is a Lipschitz function revealed at the end of iteration t. Building on previous work, we propose a generalized Hedge algorithm and show a O(\sqrtt \log t) bound on the regret when the losses are uniformly Lipschitz and S is uniformly fat (a weaker condition than convexity). Finally, we propose a generalization to the dual averaging method on the set of Lebesgue-continuous distributions over S.}
}