Minimizing Dynamic Regret and Adaptive Regret Simultaneously

Lijun Zhang, Shiyin Lu, Tianbao Yang
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:309-319, 2020.

Abstract

Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regret have been proposed to guide the design of online algorithms. The former one aims to minimize the global regret with respect to a sequence of changing comparators, and the latter one attempts to minimize every local regret with respect to a fixed comparator. Existing algorithms for dynamic regret and adaptive regret are developed independently, and only target one performance measure. In this paper, we bridge this gap by proposing novel online algorithms that are able to minimize the dynamic regret and adaptive regret simultaneously. In fact, our theoretical guarantee is even stronger in the sense that one algorithm is able to minimize the dynamic regret over any interval.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-zhang20a, title = {Minimizing Dynamic Regret and Adaptive Regret Simultaneously}, author = {Zhang, Lijun and Lu, Shiyin and Yang, Tianbao}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {309--319}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/zhang20a/zhang20a.pdf}, url = { http://proceedings.mlr.press/v108/zhang20a.html }, abstract = {Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regret have been proposed to guide the design of online algorithms. The former one aims to minimize the global regret with respect to a sequence of changing comparators, and the latter one attempts to minimize every local regret with respect to a fixed comparator. Existing algorithms for dynamic regret and adaptive regret are developed independently, and only target one performance measure. In this paper, we bridge this gap by proposing novel online algorithms that are able to minimize the dynamic regret and adaptive regret simultaneously. In fact, our theoretical guarantee is even stronger in the sense that one algorithm is able to minimize the dynamic regret over any interval.} }
Endnote
%0 Conference Paper %T Minimizing Dynamic Regret and Adaptive Regret Simultaneously %A Lijun Zhang %A Shiyin Lu %A Tianbao Yang %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-zhang20a %I PMLR %P 309--319 %U http://proceedings.mlr.press/v108/zhang20a.html %V 108 %X Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regret have been proposed to guide the design of online algorithms. The former one aims to minimize the global regret with respect to a sequence of changing comparators, and the latter one attempts to minimize every local regret with respect to a fixed comparator. Existing algorithms for dynamic regret and adaptive regret are developed independently, and only target one performance measure. In this paper, we bridge this gap by proposing novel online algorithms that are able to minimize the dynamic regret and adaptive regret simultaneously. In fact, our theoretical guarantee is even stronger in the sense that one algorithm is able to minimize the dynamic regret over any interval.
APA
Zhang, L., Lu, S. & Yang, T.. (2020). Minimizing Dynamic Regret and Adaptive Regret Simultaneously. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:309-319 Available from http://proceedings.mlr.press/v108/zhang20a.html .

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