Adaptive Maximization of Social Welfare

Nicolò Cesa-Bianchi, Roberto Colomboni and Maximilian Kasy

No 11259, CESifo Working Paper Series from CESifo

Abstract: 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 multi-armed 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).

Keywords: optimal taxation; multi-armed bandits; experimental design (search for similar items in EconPapers)
JEL-codes: C73 C90 H21 (search for similar items in EconPapers)
Date: 2024
New Economics Papers: this item is included in nep-des and nep-pbe
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Related works:
Working Paper: Adaptive maximization of social welfare (2024)
Working Paper: Adaptive Maximization of Social Welfare (2024)
Working Paper: Adaptive Maximization of Social Welfare (2024)
Working Paper: Adaptive Maximization of Social Welfare (2024)
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