Adaptive maximization of social welfare
This work addresses the challenge of adaptive policy optimization in social welfare contexts, such as taxation, but is incremental as it builds on existing bandit algorithms and regret analysis.
The paper tackles the problem of repeatedly choosing policies to maximize social welfare, which combines private utility and public revenue, by learning response functions through experimentation. It derives a lower bound on regret and shows that a variant of the Exp3 algorithm achieves an optimal cumulative regret rate of T^{2/3} in adversarial settings, while a dyadic search algorithm achieves T^{1/2} in stochastic settings with concave welfare.
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 $T^{2/3}$. This implies that (i) welfare maximization is harder than the multi-armed bandit problem (with a rate of $T^{1/2}$ 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 $T^{1/2}$ (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).