Adaptive strategies in Kelly's horse races model. (1st September 2022)

• Record Type: Journal Article
• Authors: Despons, Armand; Peliti, Luca; Lacoste, David
• Is Part Of: Journal of statistical mechanics. (2022:Sep.)
• Publication Date: 2022-09-01
• Subjects: learning theory -- statistical inference -- optimization under uncertainty -- game theory; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac8e58
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. We characterize the cost of this gambling strategy and we analyze the asymptotic scaling of the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler's regret. We also explain how this adaptive strategy relates to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits the information contained in the bookmaker odds distribution.