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Simchi-Levi, David Ai, Rui Massachusetts Institute of Technology. Institute for Data, Systems, and Society 2025-11-05T19:33:20Z 2025-11-05T19:33:20Z 2025-05 2025-07-16T16:02:27.376Z https://hdl.handle.net/1721.1/163541 https://orcid.org/0009-0005-9262-0630 The independence axiom (IA) proposed by Von Neumann and Morgenstern [50] is the cornerstone of the expected utility theory. However, some empirical experiments show that the IA is often violated in the real world. We propose a new kind of multi-armed bandit problem where the expectation of outcomes may influence the agent’s utility which we call expectation-dependent multi-armed bandits and rationalize the choice of agents in Machina’s paradox lacking the IA. We design provably efficient algorithms with low minimax regrets and show their consistency of time horizon T with corresponding regret lower bounds, revealing statistical optimality. Furthermore, as we first consider bandits whose corresponding utility depends on both reality and expectation, it provides a bridge between machine learning and economic behavior theory, shedding light on how to interpret some counterintuitive economic scenarios, like bounded rationality explored by Zhang et al. [54]. S.M. Massachusetts Institute of Technology Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ Problem-Independent Regrets on Expectation-Dependent Multi-Armed Bandits Thesis application/pdf Master Master of Science in Social and Engineering Systems Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="d87b3a95-2582-4605-b634-0947b999c16c"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Title>Problem-Independent Regrets on Expectation-Dependent Multi-Armed Bandits</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2025-05</PublicationDate> <Authors> <Author> <DisplayName>Ai, Rui</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>https://creativecommons.org/licenses/by-nc-nd/4.0/</License> <Abstract>The independence axiom (IA) proposed by Von Neumann and Morgenstern [50] is the cornerstone of the expected utility theory. However, some empirical experiments show that the IA is often violated in the real world. We propose a new kind of multi-armed bandit problem where the expectation of outcomes may influence the agent’s utility which we call expectation-dependent multi-armed bandits and rationalize the choice of agents in Machina’s paradox lacking the IA. We design provably efficient algorithms with low minimax regrets and show their consistency of time horizon T with corresponding regret lower bounds, revealing statistical optimality. Furthermore, as we first consider bandits whose corresponding utility depends on both reality and expectation, it provides a bridge between machine learning and economic behavior theory, shedding light on how to interpret some counterintuitive economic scenarios, like bounded rationality explored by Zhang et al. [54].</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>