Learning in Random Utility Models Via Online Decision Problems

TL;DR

This paper introduces a gradient-based online learning algorithm for Random Utility Models, proving its consistency and linking it to established online optimization methods, with applications in game theory and behavioral modeling.

Contribution

It develops a novel online decision-making algorithm for RUMs, demonstrating Hannan consistency and equivalence to FTRL, advancing understanding of learning dynamics in stochastic choice.

Findings

Proves Hannan consistency for a broad class of RUMs.

Shows the algorithm is equivalent to Follow-The-Regularized-Leader.

Applications include modeling recency bias and equilibria in games.

Abstract

This paper examines the Random Utility Model (RUM) in repeated stochastic choice settings where decision-makers lack full information about payoffs. We propose a gradient-based learning algorithm that embeds RUM into an online decision-making framework. Our analysis establishes Hannan consistency for a broad class of RUMs, meaning the average regret relative to the best fixed action in hindsight vanishes over time. We also show that our algorithm is equivalent to the Follow-The-Regularized-Leader (FTRL) method, offering an economically grounded approach to online optimization. Applications include modeling recency bias and characterizing coarse correlated equilibria in normal-form games