论文标题
遗憾的界限和实验设计，用于估计到优化
Regret Bounds and Experimental Design for Estimate-then-Optimize
论文作者
论文摘要
在实际应用中，数据用于分两个步骤做出决策：估计和优化。首先，机器学习模型估计了将决策与结果相关的结构模型的参数。其次，选择了一个决定来优化结构模型的预测结果，就好像其参数正确估计一样。由于其灵活性和简单的实现，这种``估算 - 优化''方法通常用于数据驱动的决策。估计步骤中的错误可以引导估计值，然后优化到最佳决策，从而导致遗憾，即做出的决策与最佳决策之间的价值差异，并了解结构模型的参数。我们为这种遗憾提供了一本小说，以解决平稳和不受约束的优化问题。使用此界限，在估计参数是次高斯随机向量的线性变换的设置中，我们为实验设计提供了一般的程序，以最大程度地减少估计值 - 最佳化的遗憾。我们在简单的例子和大流行控制应用上演示了我们的方法。
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.
