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PAC-Bayesian Treatment Allocation Under Budget Constraints

Daniel F. Pellatt

arXiv 18 Dec 2022 · Econometrics

arXiv:2212.09007 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper considers the estimation of treatment assignment rules when the policy maker faces a general budget or resource constraint. Utilizing the PAC-Bayesian framework, we propose new treatment assignment rules that allow for flexible notions of treatment outcome, treatment cost, and a budget constraint. For example, the constraint setting allows for cost-savings, when the costs of non-treatment exceed those of treatment for a subpopulation, to be factored into the budget. It also accommodates simpler settings, such as quantity constraints, and doesn't require outcome responses and costs to have the same unit of measurement. Importantly, the approach accounts for settings where budget or resource limitations may preclude treating all that can benefit, where costs may vary with individual characteristics, and where there may be uncertainty regarding the cost of treatment rules of interest. Despite the nomenclature, our theoretical analysis examines frequentist properties of the proposed rules. For stochastic rules that typically approach budget-penalized empirical welfare maximizing policies in larger samples, we derive non-asymptotic generalization bounds for the target population costs and sharp oracle-type inequalities that compare the rules' welfare regret to that of optimal policies in relevant budget categories. A closely related, non-stochastic, model aggregation treatment assignment rule is shown to inherit desirable attributes.

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52
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in-text mentions
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appendix boundary found by appendix_titled_section at “Appendix A: Proofs\label{sec: Appendix}” · 54% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Kitagawa, T. and Tetenov, A (2018) Who should be treated? empirical welfare maximization methods for treatment choice1.000135100%
2Sun, L (2021) Empirical welfare maximization with constraints1.00063100%
3Catoni, O (2007) Pac-bayesian supervised classification: The thermodynamics of statistical learning1.00053100%
4Sun, H., Du, S., and Wager, S (2021) Treatment allocation under uncertain costs0.97112592%
5Mbakop, E. and Tabord-Meehan, M (2021) Model selection for treatment choice: Penalized welfare maximization0.92843100%
6Alquier, P., Ridgway, J., and Chopin, N (2016) On the properties of variational approximations of gibbs posteriors0.9209678%
7Lever, G., Laviolette, F., and Shawe-Taylor, J (2010) Distribution-dependent pac-bayes priors0.7547343%
8Seeger, M (2002) Pac-bayesian generalisation error bounds for gaussian process classification0.7375340%
9Bhattacharya, D. and Dupas, P (2012) Inferring welfare maximizing treatment assignment under budget constraints0.73732100%
10Manski, C. F (2004) Statistical treatment rules for heterogeneous populations0.73732100%

Showing the top 10 of 52 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Stochastic treatment choice with empirical welfare updating0.40511