Bandit Convex Optimization in Non-stationary Environments

Peng Zhao, Guanghui Wang, Lijun Zhang, Zhi-Hua Zhou
; Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:1508-1518, 2020.

Abstract

Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the dynamic regret as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T^{3/4}(1+P_T)^{1/2})$ and $O(T^{1/2}(1+P_T)^{1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $\Omega(T^{1/2}(1+P_T)^{1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-zhao20b, title = {Bandit Convex Optimization in Non-stationary Environments}, author = {Zhao, Peng and Wang, Guanghui and Zhang, Lijun and Zhou, Zhi-Hua}, pages = {1508--1518}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, address = {Online}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/zhao20b/zhao20b.pdf}, url = {http://proceedings.mlr.press/v108/zhao20b.html}, abstract = {Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the dynamic regret as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T^{3/4}(1+P_T)^{1/2})$ and $O(T^{1/2}(1+P_T)^{1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $\Omega(T^{1/2}(1+P_T)^{1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.} }
Endnote
%0 Conference Paper %T Bandit Convex Optimization in Non-stationary Environments %A Peng Zhao %A Guanghui Wang %A Lijun Zhang %A Zhi-Hua Zhou %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-zhao20b %I PMLR %J Proceedings of Machine Learning Research %P 1508--1518 %U http://proceedings.mlr.press %V 108 %W PMLR %X Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the dynamic regret as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T^{3/4}(1+P_T)^{1/2})$ and $O(T^{1/2}(1+P_T)^{1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $\Omega(T^{1/2}(1+P_T)^{1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.
APA
Zhao, P., Wang, G., Zhang, L. & Zhou, Z.. (2020). Bandit Convex Optimization in Non-stationary Environments. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in PMLR 108:1508-1518

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