{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/heteroscedastic-bandits-with-reneging","title":"Stay With Me: Lifetime Maximization Through Heteroscedastic Linear Bandits With Reneging","arxiv_id":"1810.12418","date":"2018-10-29","proceeding":null,"authors":["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.","url_abs":"https://arxiv.org/abs/1810.12418v4","url_pdf":"https://arxiv.org/pdf/1810.12418v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"heteroscedastic-bandits-with-reneging","repo_url":"https://github.com/Xi-Liu/heteroscedasticbandits","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"multi-armed-bandits","task_name":"Multi-Armed Bandits"},{"task_slug":"sequential-decision-making","task_name":"Sequential Decision Making"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}