论文标题
在功能和功能估计中纠正凸性偏差
Correcting Convexity Bias in Function and Functional Estimate
论文作者
论文摘要
提出了一系列不同方法的一般框架，以提高凸函数（或功能）值的估计值时，只有对真实输入的嘈杂观察结果。从技术上讲，我们的方法捕获了凸性引入的偏见，并从基线估计值中消除了这种偏见。进行理论分析以表明所提出的方法可以严格减少在轻度条件下的预期估计误差。应用时，这些方法不需要有关问题的具体知识，除了函数的凸度和评估。因此，它们可以用作现成的工具，以获得有关广泛问题的良好估计，包括具有随机目标函数或约束的优化问题，以及概率分布的功能，例如熵和Wasserstein距离。关于各种问题的数值实验表明，与基线方法相比，我们的方法可以显着提高估计值的质量。
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias introduced by the convexity and remove this bias from a baseline estimate. Theoretical analysis are conducted to show that the proposed methods can strictly reduce the expected estimate error under mild conditions. When applied, the methods require no specific knowledge about the problem except the convexity and the evaluation of the function. Therefore, they can serve as off-the-shelf tools to obtain good estimate for a wide range of problems, including optimization problems with random objective functions or constraints, and functionals of probability distributions such as the entropy and the Wasserstein distance. Numerical experiments on a wide variety of problems show that our methods can significantly improve the quality of the estimate compared with the baseline method.
