A Simple Online Algorithm for Competing with Dynamic Comparators

Yu-Jie Zhang, Peng Zhao, Zhi-Hua Zhou
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:390-399, 2020.

Abstract

Online learning in dynamic environments has recently drawn considerable attention, where dynamic regret is usually employed to compare decisions of online algorithms to dynamic comparators. In previous works, dynamic regret bounds are typically established in terms of regularity of comparators $C_T$ or that of online functions $V_T$. Recently, Jadbabaie et al. [2015] propose an algorithm that can take advantage of both regularities and enjoy an $\tilde{O}(\sqrt{1+D_T} + \min\{\sqrt{(1+D_T)C_T}, (1+D_T)^{1/3}V_T^{1/3}T^{1/3}\})$ dynamic regret, where $D_T$ is an additional quantity to measure the niceness of environments. The regret bound adapts to the smaller regularity of problem environments and is tighter than all existing dynamic regret guarantees. Nevertheless, their algorithm involves non-convex programming at each iteration, and thus requires burdensome computations. In this paper, we design a simple algorithm based on the online ensemble, which provably enjoys the same (even slightly stronger) guarantee as the state-of-the-art rate, yet is much more efficient because our algorithm does not involve any non-convex problem solving. Empirical studies also verify the efficacy and efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-zhang20a, title = {A Simple Online Algorithm for Competing with Dynamic Comparators}, author = {Zhang, Yu-Jie and Zhao, Peng and Zhou, Zhi-Hua}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {390--399}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/zhang20a/zhang20a.pdf}, url = {https://proceedings.mlr.press/v124/zhang20a.html}, abstract = {Online learning in dynamic environments has recently drawn considerable attention, where dynamic regret is usually employed to compare decisions of online algorithms to dynamic comparators. In previous works, dynamic regret bounds are typically established in terms of regularity of comparators $C_T$ or that of online functions $V_T$. Recently, Jadbabaie et al. [2015] propose an algorithm that can take advantage of both regularities and enjoy an $\tilde{O}(\sqrt{1+D_T} + \min\{\sqrt{(1+D_T)C_T}, (1+D_T)^{1/3}V_T^{1/3}T^{1/3}\})$ dynamic regret, where $D_T$ is an additional quantity to measure the niceness of environments. The regret bound adapts to the smaller regularity of problem environments and is tighter than all existing dynamic regret guarantees. Nevertheless, their algorithm involves non-convex programming at each iteration, and thus requires burdensome computations. In this paper, we design a simple algorithm based on the online ensemble, which provably enjoys the same (even slightly stronger) guarantee as the state-of-the-art rate, yet is much more efficient because our algorithm does not involve any non-convex problem solving. Empirical studies also verify the efficacy and efficiency.} }
Endnote
%0 Conference Paper %T A Simple Online Algorithm for Competing with Dynamic Comparators %A Yu-Jie Zhang %A Peng Zhao %A Zhi-Hua Zhou %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-zhang20a %I PMLR %P 390--399 %U https://proceedings.mlr.press/v124/zhang20a.html %V 124 %X Online learning in dynamic environments has recently drawn considerable attention, where dynamic regret is usually employed to compare decisions of online algorithms to dynamic comparators. In previous works, dynamic regret bounds are typically established in terms of regularity of comparators $C_T$ or that of online functions $V_T$. Recently, Jadbabaie et al. [2015] propose an algorithm that can take advantage of both regularities and enjoy an $\tilde{O}(\sqrt{1+D_T} + \min\{\sqrt{(1+D_T)C_T}, (1+D_T)^{1/3}V_T^{1/3}T^{1/3}\})$ dynamic regret, where $D_T$ is an additional quantity to measure the niceness of environments. The regret bound adapts to the smaller regularity of problem environments and is tighter than all existing dynamic regret guarantees. Nevertheless, their algorithm involves non-convex programming at each iteration, and thus requires burdensome computations. In this paper, we design a simple algorithm based on the online ensemble, which provably enjoys the same (even slightly stronger) guarantee as the state-of-the-art rate, yet is much more efficient because our algorithm does not involve any non-convex problem solving. Empirical studies also verify the efficacy and efficiency.
APA
Zhang, Y., Zhao, P. & Zhou, Z.. (2020). A Simple Online Algorithm for Competing with Dynamic Comparators. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:390-399 Available from https://proceedings.mlr.press/v124/zhang20a.html.

Related Material