预算约束下的PAC-贝叶斯处理分配
PAC-Bayesian Treatment Allocation Under Budget Constraints
AI总结：
本文针对预算约束下的处理分配问题，提出基于PAC-贝叶斯框架的灵活分配规则，推导了随机规则的非渐近泛化界和严格oracle型不等式，并验证了非随机模型聚合规则的优良属性。
摘要：
本文研究了政策制定者面临一般预算或资源约束时的处理分配规则估计问题。利用PAC-贝叶斯框架，我们提出了新的处理分配规则，该规则可灵活适配处理结果、处理成本和预算约束的不同定义。例如，当非处理成本超过某一子群体的处理成本时，该约束设置可将成本节约纳入预算考量。它也适用于更简单的场景，如数量约束，且不要求结果响应和成本具有相同的度量单位。重要的是，该方法适用于以下场景：预算或资源限制可能导致无法为所有可受益个体提供处理，成本可能随个体特征变化，以及目标处理规则的成本可能存在不确定性。尽管名称如此，我们的理论分析考察了所提规则的频率学派性质。对于在大样本中通常趋近于预算惩罚经验福利最大化策略的随机规则，我们推导了目标群体成本的非渐近泛化界，以及将规则的福利遗憾与相关预算类别中最优策略的福利遗憾进行比较的严格oracle型不等式。一种密切相关的非随机模型聚合处理分配规则被证明继承了这些优良属性。
英文摘要：
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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