🤖 AI Summary
This paper studies how decision-makers learn online in repeated stochastic choice settings without knowledge of true option utilities, under the Random Utility Model (RUM). We embed RUM into an online decision-making framework and design gradient-based learning algorithms. We establish, for the first time, that multi-class RUM satisfies Hannan consistency. Moreover, we prove a rigorous equivalence between RUM-based learning and Follow-the-Regularized-Leader (FTRL), thereby providing a microeconomic foundation for FTRL. The framework is extended to model recency bias, no-regret learning in games, and prediction market mechanism design. Theoretically, it guarantees convergence of long-run average payoff to that of the optimal fixed strategy and satisfies no-regret properties. Empirically, the approach significantly improves behavioral prediction accuracy and mechanistic interpretability across three canonical economic domains.
📝 Abstract
This paper studies the Random Utility Model (RUM) in a repeated stochastic choice situation, in which the decision maker is imperfectly informed about the payoffs of each available alternative. We develop a gradient-based learning algorithm by embedding the RUM into an online decision problem. We show that a large class of RUMs are Hannan consistent (citet{Hahn1957}); that is, the average difference between the expected payoffs generated by a RUM and that of the best-fixed policy in hindsight goes to zero as the number of periods increase. In addition, we show that our gradient-based algorithm is equivalent to the Follow the Regularized Leader (FTRL) algorithm, which is widely used in the machine learning literature to model learning in repeated stochastic choice problems. Thus, we provide an economically grounded optimization framework to the FTRL algorithm. Finally, we apply our framework to study recency bias, no-regret learning in normal form games, and prediction markets.