Efficient Contextual Bandits in Non-stationary Worlds

Haipeng Luo, Chen-Yu Wei, Alekh Agarwal, John Langford
Proceedings of the 31st Conference On Learning Theory, PMLR 75:1739-1776, 2018.

Abstract

Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution. We analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When competing with the best policy at each time, one of our algorithms achieves regret $\mathcal{O}(\sqrt{ST})$ if there are $T$ rounds with $S$ stationary periods, or more generally $\mathcal{O}(\Delta^{1/3}T^{2/3})$ where $\Delta$ is some non-stationarity measure. These results almost match the optimal guarantees achieved by an inefficient baseline that is a variant of the classic Exp4 algorithm. The dynamic regret result is also the first one for efficient and fully adversarial contextual bandit. Furthermore, while the results above require tuning a parameter based on the unknown quantity $S$ or $\Delta$, we also develop a parameter free algorithm achieving regret $\min\{S^{1/4}T^{3/4}, \Delta^{1/5}T^{4/5}\}$. This improves and generalizes the best existing result $\Delta^{0.18}T^{0.82}$ by Karnin and Anava (2016) which only holds for the two-armed bandit problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v75-luo18a, title = {Efficient Contextual Bandits in Non-stationary Worlds}, author = {Luo, Haipeng and Wei, Chen-Yu and Agarwal, Alekh and Langford, John}, booktitle = {Proceedings of the 31st Conference On Learning Theory}, pages = {1739--1776}, year = {2018}, editor = {Bubeck, Sébastien and Perchet, Vianney and Rigollet, Philippe}, volume = {75}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v75/luo18a/luo18a.pdf}, url = {https://proceedings.mlr.press/v75/luo18a.html}, abstract = {Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution. We analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When competing with the best policy at each time, one of our algorithms achieves regret $\mathcal{O}(\sqrt{ST})$ if there are $T$ rounds with $S$ stationary periods, or more generally $\mathcal{O}(\Delta^{1/3}T^{2/3})$ where $\Delta$ is some non-stationarity measure. These results almost match the optimal guarantees achieved by an inefficient baseline that is a variant of the classic Exp4 algorithm. The dynamic regret result is also the first one for efficient and fully adversarial contextual bandit. Furthermore, while the results above require tuning a parameter based on the unknown quantity $S$ or $\Delta$, we also develop a parameter free algorithm achieving regret $\min\{S^{1/4}T^{3/4}, \Delta^{1/5}T^{4/5}\}$. This improves and generalizes the best existing result $\Delta^{0.18}T^{0.82}$ by Karnin and Anava (2016) which only holds for the two-armed bandit problem.} }
Endnote
%0 Conference Paper %T Efficient Contextual Bandits in Non-stationary Worlds %A Haipeng Luo %A Chen-Yu Wei %A Alekh Agarwal %A John Langford %B Proceedings of the 31st Conference On Learning Theory %C Proceedings of Machine Learning Research %D 2018 %E Sébastien Bubeck %E Vianney Perchet %E Philippe Rigollet %F pmlr-v75-luo18a %I PMLR %P 1739--1776 %U https://proceedings.mlr.press/v75/luo18a.html %V 75 %X Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution. We analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When competing with the best policy at each time, one of our algorithms achieves regret $\mathcal{O}(\sqrt{ST})$ if there are $T$ rounds with $S$ stationary periods, or more generally $\mathcal{O}(\Delta^{1/3}T^{2/3})$ where $\Delta$ is some non-stationarity measure. These results almost match the optimal guarantees achieved by an inefficient baseline that is a variant of the classic Exp4 algorithm. The dynamic regret result is also the first one for efficient and fully adversarial contextual bandit. Furthermore, while the results above require tuning a parameter based on the unknown quantity $S$ or $\Delta$, we also develop a parameter free algorithm achieving regret $\min\{S^{1/4}T^{3/4}, \Delta^{1/5}T^{4/5}\}$. This improves and generalizes the best existing result $\Delta^{0.18}T^{0.82}$ by Karnin and Anava (2016) which only holds for the two-armed bandit problem.
APA
Luo, H., Wei, C., Agarwal, A. & Langford, J.. (2018). Efficient Contextual Bandits in Non-stationary Worlds. Proceedings of the 31st Conference On Learning Theory, in Proceedings of Machine Learning Research 75:1739-1776 Available from https://proceedings.mlr.press/v75/luo18a.html.

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