  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.
