Stay With Me: Lifetime Maximization Through Heteroscedastic Linear Bandits With Reneging
Ping-Chun Hsieh, Xi Liu, Anirban Bhattacharya, P R Kumar
Abstract
Sequential decision making for lifetime maximization is a critical problem in many real-world applications, such as medical treatment and portfolio selection. In these applications, a “reneging” phenomenon, where participants may disengage from future interactions after observing an unsatisfiable outcome, is rather prevalent. To address the above issue, this paper proposes a model of heteroscedastic linear bandits with reneging, which allows each participant to have a distinct “satisfaction level," with any interaction outcome falling short of that level resulting in that participant reneging. Moreover, it allows the variance of the outcome to be context-dependent. Based on this model, we develop a UCB-type policy, namely HR-UCB, and prove that it achieves $\mathcal{O}\big(\sqrt{{T}(\log({T}))^{3}}\big)$ regret. Finally, we validate the performance of HR-UCB via simulations.
BibTeX
@InProceedings{pmlr-v97-hsieh19a,
title = {Stay With Me: Lifetime Maximization Through Heteroscedastic Linear Bandits With Reneging},
author = {Hsieh, Ping-Chun and Liu, Xi and Bhattacharya, Anirban and Kumar, P R},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {2800--2809},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/hsieh19a/hsieh19a.pdf},
url = {https://proceedings.mlr.press/v97/hsieh19a.html},
abstract = {Sequential decision making for lifetime maximization is a critical problem in many real-world applications, such as medical treatment and portfolio selection. In these applications, a “reneging” phenomenon, where participants may disengage from future interactions after observing an unsatisfiable outcome, is rather prevalent. To address the above issue, this paper proposes a model of heteroscedastic linear bandits with reneging, which allows each participant to have a distinct “satisfaction level," with any interaction outcome falling short of that level resulting in that participant reneging. Moreover, it allows the variance of the outcome to be context-dependent. Based on this model, we develop a UCB-type policy, namely HR-UCB, and prove that it achieves $\mathcal{O}\big(\sqrt{{T}(\log({T}))^{3}}\big)$ regret. Finally, we validate the performance of HR-UCB via simulations.}
}