Problem-Independent Regrets on Expectation-Dependent Multi-Armed Bandits

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].

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Institute for Data, Systems, and Society

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2025

Author dc:creator

• Ai, Rui

Advisor dc:contributor.advisor

• Simchi-Levi, David

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/163541

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/163541