Nicolo Cesa-Bianchi, Roberto Colomboni, Maximilian Kasy
arXiv 14 Oct 2023 · Econometrics · publishedEconometrica (2025) · 2 citations (OpenAlex)
arXiv:2310.09597 · PDF · DOI · OpenAlex · Extracted main text
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).
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ramsey, F. P (1927) A contribution to the theory of taxation | 1.000 | 5 | 3 | 100% |
| 2 | Mirrlees, J (1971) An exploration in the theory of optimum income taxation | 0.811 | 4 | 2 | 100% |
| 3 | Saez, E (2001) Using elasticities to derive optimal income tax rates | 0.811 | 4 | 2 | 100% |
| 4 | Cesa-Bianchi, N., Cesari, T., Colomboni, R., Fusco, F., and Leonardi… (2024) Bilateral trade: A regret minimization perspective self | 0.737 | 3 | 2 | 100% |
| 5 | Chetty, R (2009) Sufficient statistics for welfare analysis: A bridge between structural and reduced-form methods | 0.737 | 3 | 2 | 100% |
| 6 | Kleinberg, R. D. and Leighton, F. T (2003) The value of knowing a demand curve: Bounds on regret for online posted-price auctions | 0.737 | 3 | 2 | 100% |
| 7 | Lattimore, T. and Szepesvári, C (2020) Bandit algorithms | 0.737 | 3 | 2 | 100% |
| 8 | Auer, P., Cesa-Bianchi, N., Freund, Y., and Schapire, R. E (2002) The nonstochastic multiarmed bandit problem self | 0.644 | 2 | 2 | 100% |
| 9 | Cesa-Bianchi, N., Cesari, T. R., Colomboni, R., Fusco, F., and Leona… (2023) Repeated bilateral trade against a smoothed adversary self | 0.644 | 2 | 2 | 100% |
| 10 | den Boer, A. V (2015) Dynamic pricing and learning: historical origins, current research, and new directions | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 61 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence | 0.644 | 2 | 2 |
| 2 | Batched Adaptive Network Formation | 0.405 | 1 | 1 |