Matching Markets meet Cumulative Prospect Theory: Towards Optimal and Adversarially Robust Learning

2026-06-18

AI Summary

This study addresses the multi-agent multi-armed bandit problem in competitive two-sided matching markets, incorporating cumulative prospect theory (CPT) for the first time to model human nonlinear risk preferences under adversarial reward corruption. The authors propose an adaptive exploration strategy that integrates an α-Hölder continuous weighting function with a stable matching mechanism, achieving logarithmic robust regret bounds under both known and unknown corruption budgets. Their key contributions include establishing a player-optimal regret bound of 𝒪(K log T (1/Δ)^{2/α}) and, when the number of arms K significantly exceeds the number of agents N, further eliminating the dependence on K in the leading term to obtain a logarithmic regret guarantee independent of K.

Abstract

We study a multi-agent multi-armed bandit problem in the competitive setup with two-sided matching markets under a human centric decision making model. To capture human preferences, we use cumulative prospect theory (CPT) that weighs the actions of the agent in a nonlinear fashion using a ($α$-Hölder continuous) weight function. CPT has been widely used in behavioral economics and risk sensitive machine learning to emulate human preferences. We analyze the state-of-the-art learning algorithm with CPT weight distorted rewards and obtain a player optimal regret of $\mathcal{O}(K\log T \left(\frac{1}Δ\right)^{2/α})$, where $K$ denotes the number of arms, $T$ is the learning horizon, and $Δ$ represents (suitably defined) players' minimum preference gap. Noticing the dependence on $Δ$ to be sub-optimal, we further improve this regret by judiciously selecting the active set of arms during exploration, which removes the dependence on $K$ in the dominant term and achieves an improved (optimal) regret guarantees in the setting where the number of arms $K$ is significantly larger than the number of players $N$. In addition, we consider adversarial markets where the observed rewards of the agents may be corrupted. We propose and analyze algorithms for robust markets with CPT as risk sensitive measure in both settings where the total corruption budget is known and where it is unknown, and establish logarithmic player-optimal regret guarantees in both cases.

Problem

• Matching Markets
• Cumulative Prospect Theory
• Multi-agent Multi-armed Bandit
• Adversarial Robustness
• Human-centric Decision Making

Innovation

• Cumulative Prospect Theory
• Matching Markets
• Adversarially Robust Learning
• Multi-agent Multi-armed Bandits
• Player-optimal Regret