Penalized FTRL with Time-Varying Constraints
Abstract
In this paper we extend the classical Follow-The-Regularized-Leader (FTRL) algorithm to encompass time-varying constraints, through adaptive penalization. We establish sufficient conditions for the proposed Penalized FTRL algorithm to achieve $\mathcal O(\sqrt{t})$ O ( t ) regret and violation with respect to a strong benchmark $\hat{X}^{max}_t$ X ^ t max . Lacking prior knowledge of the constraints, this is probably the largest benchmark set that we can reasonably hope for. Our sufficient conditions are necessary in the sense that when they are violated there exist examples where $\mathcal O(\sqrt{t})$ O ( t ) regret and violation is not achieved. Compared to the best existing primal-dual algorithms, Penalized FTRL substantially extends the class of problems for which $\mathcal O(\sqrt{t})$ O ( t ) regret and violation performance is achievable.
Cite
Text
Leith and Iosifidis. "Penalized FTRL with Time-Varying Constraints." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2022. doi:10.1007/978-3-031-26419-1_19Markdown
[Leith and Iosifidis. "Penalized FTRL with Time-Varying Constraints." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2022.](https://mlanthology.org/ecmlpkdd/2022/leith2022ecmlpkdd-penalized/) doi:10.1007/978-3-031-26419-1_19BibTeX
@inproceedings{leith2022ecmlpkdd-penalized,
title = {{Penalized FTRL with Time-Varying Constraints}},
author = {Leith, Douglas J. and Iosifidis, George},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2022},
pages = {311-326},
doi = {10.1007/978-3-031-26419-1_19},
url = {https://mlanthology.org/ecmlpkdd/2022/leith2022ecmlpkdd-penalized/}
}