2023/10/14 by Nicolo Cesa-Bianchi, Nicolò Cesa‐Bianchi, Roberto Colomboni +4 · 1 voice · 1 citation
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Bandit Algorithms Research #Auction Theory and Applications #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Smart Grid Energy Management #cs.LG #econ.EM #stat.ML
paper · pdf · doi:10.48550/arxiv.2310.09597
openalex publication_date 2023/10/14 · arxiv published 2023/10/14 · arxiv updated 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).