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arXiv · 1810.12418

Stay With Me: Lifetime Maximization Through Heteroscedastic Linear Bandits With Reneging

Ping-Chun Hsieh·Xi Liu·Anirban Bhattacharya·P. R. Kumar
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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.

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Ping-Chun Hsieh, Xi Liu, Anirban Bhattacharya, P. R. Kumar. 2018-10-29. Stay With Me: Lifetime Maximization Through Heteroscedastic Linear Bandits With Reneging. https://arxiv.org/abs/1810.12418

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