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PAC-Bayesian Treatment Allocation Under Budget Constraints

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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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Working Paper

Binary Forecast and Decision Rules via PAC Bayesian Model Aggregation (with Yixiao Sun)

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We consider a PAC-Bayesian model aggregation approach to binary decision or forecast rules when different decision-outcome pairs may have asymmetric payoffs that can vary with observed covariates. The approach estimates a probability distribution over a class of models from which majority vote or stochastic decision rules can be derived. Adopting a utility-based measure of loss considered in (Granger and Machina, 2006), we show the PAC-Bayesian methodology is well suited to this setting. Non-asymptotic training sample bounds and oracle inequalities familiar in form to counterparts from the 0/1-loss literature are derived for the utility-based setting. The decision rules perform competitively in simulation experiments, achieving higher expected utility than several methods proposed in recent literature. The approach is also well suited to data-rich modeling environments; a constrained version of the learning algorithm produces utility-oriented decision rules with similarities to support vector machines.

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Publications

Pellatt, D. F., & Sun, Y. (2022). Asymptotic F test in regressions with observations collected at high frequency over long span. Journal of Econometrics. doi: 10.1016/j.jeconom.2022.10.007

Aue A, Horvath L, Pellatt DF. (2017) Functional generalized autoregressive conditional heteroscedasticity. J. Time Ser. Anal, 38:3-21. doi: 10.1111/jtsa.12192