英文标题：
《Sequential Design for Ranking Response Surfaces》
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作者：
Ruimeng Hu and Mike Ludkovski
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最新提交年份：
2016
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英文摘要：
We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given $L \\ge 2$ response surfaces over a continuous input space $\\cal X$, the aim is to efficiently find the index of the minimal response across the entire $\\cal X$. The response surfaces are not known and have to be noisily sampled one-at-a-time. This setting is motivated by stochastic control applications and requires joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging surrogates. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.
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中文摘要：
针对多个响应面排序问题，提出并分析了序贯设计方法。也就是说，给定连续输入空间$\\cal X$上的$L\\ge 2$响应曲面，目的是高效地找到整个$\\cal X$上最小响应的索引。响应面未知，必须一次一个地进行噪音采样。这种设置受随机控制应用的驱动，需要在空间和响应指数维度上进行联合实验设计。为了生成序贯设计启发式，我们研究了逐步减少不确定性的方法，以及基于后验分类复杂性的抽样。我们还将我们的连续输入公式与多武装匪徒中纯粹后悔的离散框架联系起来。为了对响应面建模，我们使用克里格替代项。文中给出了几个使用合成数据和流行病控制问题的数值例子，以说明我们的方法和各自自适应设计的有效性。
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分类信息：

一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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