Adaptive Maximization of Social Welfare

• 成果类型: Article
• 署名作者: Cesa-Bianchi, Nicolo; Colomboni, Roberto; Kasy, Maximilian
• 署名单位: University of Milan; Polytechnic University of Milan; University of Oxford
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA22351
• 发表日期: 2025
• 页码: 1073-1104
• 关键词: Regret; algorithms

摘要

We consider the problem of repeatedly choosing policies to maximize social welfare. Welfare is a weighted sum of private utility and public revenue. Earlier outcomes inform later policies. Utility is not observed, but indirectly inferred. Response functions are learned through experimentation.We derive a lower bound on regret, and a matching adversarial upper bound for a variant of the Exp3 algorithm. Cumulative regret grows at a rate of T2/3. This implies that (i) welfare maximization is harder than the multiarmed bandit problem (with a rate of T1/2 for finite policy sets), and (ii) our algorithm achieves the optimal rate. For the stochastic setting, if social welfare is concave, we can achieve a rate of T1/2 (for continuous policy sets), using a dyadic search algorithm.We analyze an extension to nonlinear income taxation, and sketch an extension to commodity taxation. We compare our setting to monopoly pricing (which is easier), and price setting for bilateral trade (which is harder).