Online Optimization : Competing with Dynamic Comparators
Ali Jadbabaie, Alexander Rakhlin, Shahin Shahrampour, Karthik Sridharan
Abstract
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop prediction methods that perform well against complex benchmarks. In this paper, we address these two directions together. We present a fully adaptive method that competes with dynamic benchmarks in which regret guarantee scales with regularity of the sequence of cost functions and comparators. Notably, the regret bound adapts to the smaller complexity measure in the problem environment. Finally, we apply our results to drifting zero-sum, two-player games where both players achieve no regret guarantees against best sequences of actions in hindsight.
BibTeX
@InProceedings{pmlr-v38-jadbabaie15,
title = {{Online Optimization : Competing with Dynamic Comparators}},
author = {Jadbabaie, Ali and Rakhlin, Alexander and Shahrampour, Shahin and Sridharan, Karthik},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {398--406},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/jadbabaie15.pdf},
url = {https://proceedings.mlr.press/v38/jadbabaie15.html},
abstract = {Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop prediction methods that perform well against complex benchmarks. In this paper, we address these two directions together. We present a fully adaptive method that competes with dynamic benchmarks in which regret guarantee scales with regularity of the sequence of cost functions and comparators. Notably, the regret bound adapts to the smaller complexity measure in the problem environment. Finally, we apply our results to drifting zero-sum, two-player games where both players achieve no regret guarantees against best sequences of actions in hindsight.}
}