标题： 从不精确数据中学习一个Hölder函数的最大值 显示英文标题

标题： Learning the Maximum of a Hölder Function from Inexact Data

摘要： 在最优恢复的理论框架下，本文确定了{\em 最佳}程序，以根据通过固定数据点的不精确点评估获得的霍尔德函数来学习感兴趣的量。{\em 最佳}在这里指的是最小化最坏情况误差的程序。基本的论证暗示了处理非线性感兴趣量的可能性，特别关注函数最大值。在局部情况下，即对于固定的数据显示向量，最优程序（输出所谓的切比雪夫中心）相对于不精确评估的一般模型进行了精确描述。相对于一个稍微更受限制的模型和全局情况下，即所有数据向量上统一，提出了另一个最优程序，说明如何纠正仅仅返回数据向量最大值的自然低估。抖动数据也作为在数据点上优化的最小最坏情况误差评估的副产品进行了简要讨论。 显示英文摘要

摘要： Within the theoretical framework of Optimal Recovery, one determines in this article the {\em best} procedures to learn a quantity of interest depending on a H\"older function acquired via inexact point evaluations at fixed datasites. {\em Best} here refers to procedures minimizing worst-case errors. The elementary arguments hint at the possibility of tackling nonlinear quantities of interest, with a particular focus on the function maximum. In a local setting, i.e., for a fixed data vector, the optimal procedure (outputting the so-called Chebyshev center) is precisely described relatively to a general model of inexact evaluations. Relatively to a slightly more restricted model and in a global setting, i.e., uniformly over all data vectors, another optimal procedure is put forward, showing how to correct the natural underestimate that simply returns the data vector maximum. Jitterred data are also briefly discussed as a side product of evaluating the minimal worst-case error optimized over the datasites.