论文标题
线性函数的政策估计：半参数效率的非肌电理论
Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency
论文作者
论文摘要
在因果推理和强盗文献中，基于观察数据的线性功能估算线性功能的问题是规范的。我们分析了首先估计治疗效果函数的广泛的两阶段程序，然后使用该数量来估计线性功能。我们证明了此类程序的均方误差上的非反应上限：这些界限表明，为了获得非反应性最佳程序，估计治疗效果的误差应在特定加权的$ l^2 $ -Norm中最小化。我们根据该加权规范的约束回归分析了两阶段的程序，并通过匹配非反对局部最小值下限的有限样品中的实例依赖性最优性。这些结果表明，除了取决于渐近效率的方差外，最佳的非质子风险还取决于真实结果函数之间的加权标准距离及其近似值（由样本量支持的最丰富功能类别）之间的加权范围。
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function, and then use this quantity to estimate the linear functional. We prove non-asymptotic upper bounds on the mean-squared error of such procedures: these bounds reveal that in order to obtain non-asymptotically optimal procedures, the error in estimating the treatment effect should be minimized in a certain weighted $L^2$-norm. We analyze a two-stage procedure based on constrained regression in this weighted norm, and establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds. These results show that the optimal non-asymptotic risk, in addition to depending on the asymptotically efficient variance, depends on the weighted norm distance between the true outcome function and its approximation by the richest function class supported by the sample size.
