In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to optimize the structural model's predicted outcome as if its parameters were correctly estimated. Due to its flexibility and simple implementation, this ``estimate-then-optimize'' approach is often used for data-driven decision-making. Errors in the estimation step can lead estimate-then-optimize to sub-optimal decisions that result in regret, i.e., a difference in value between the decision made and the best decision available with knowledge of the structural model's parameters. We provide a novel bound on this regret for smooth and unconstrained optimization problems. Using this bound, in settings where estimated parameters are linear transformations of sub-Gaussian random vectors, we provide a general procedure for experimental design to minimize the regret resulting from estimate-then-optimize. We demonstrate our approach on simple examples and a pandemic control application.
翻译:在实际应用中,数据用于分两个步骤作出决定:估计和优化。首先,机器学习模型估计与结果相关决定的结构模型的估算参数。第二,选择一个决定,使结构模型的预测结果优化,仿佛其参数得到正确估计。由于其灵活性和简单的执行,“估计-当时-优化”的方法常常用于数据驱动的决策。估计步骤中的错误可以导致估计-当时-优化到导致遗憾的亚最佳决定,即所作决定的价值与掌握结构模型参数知识的最佳决定之间的差别。我们对这种遗憾提出了新颖的看法,以便解决顺利和不受限制的优化问题。在估计参数是亚-高加索随机矢量的线性转变的情况下,我们利用这一约束,为实验设计提供了一个一般程序,以尽量减少估计-当时-优化所产生的遗憾。我们展示了我们对于简单例子和大流行病控制应用的方法。