Adaptive Regret of Convex and Smooth Functions
Abstract
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time. Different from previous works that only utilize the convexity condition, this paper further exploits smoothness to improve the adaptive regret. To this end, we develop novel adaptive algorithms for convex and smooth functions, and establish problem-dependent regret bounds over any interval. Our regret bounds are comparable to existing results in the worst case, and become much tighter when the comparator has a small loss.
Cite
Text
Zhang et al. "Adaptive Regret of Convex and Smooth Functions." International Conference on Machine Learning, 2019.Markdown
[Zhang et al. "Adaptive Regret of Convex and Smooth Functions." International Conference on Machine Learning, 2019.](https://mlanthology.org/icml/2019/zhang2019icml-adaptive/)BibTeX
@inproceedings{zhang2019icml-adaptive,
title = {{Adaptive Regret of Convex and Smooth Functions}},
author = {Zhang, Lijun and Liu, Tie-Yan and Zhou, Zhi-Hua},
booktitle = {International Conference on Machine Learning},
year = {2019},
pages = {7414-7423},
volume = {97},
url = {https://mlanthology.org/icml/2019/zhang2019icml-adaptive/}
}