在线学习最小和集封面和潘多拉的盒子
Online Learning for Min Sum Set Cover and Pandora's Box
摘要：
随机优化中的两个核心问题是最小和集覆盖和潘多拉盒子。在潘多拉魔盒中，我们会看到$n$盒子，每个盒子都包含一个未知值，目标是以某种顺序打开盒子，以最小化搜索成本和找到的最小值之和。给定值向量的分布，我们被要求确定一个接近最优的搜索顺序。“最小和集覆盖”对应于值为0或无穷大的情况。在这项工作中，我们研究的情况下，值向量不是从一个分布，但在一个在线的方式呈现给学习者。我们提出了一个计算效率高的算法，是恒定的竞争力对成本的最佳搜索顺序。我们将我们的结果扩展到一个强盗设置，其中只有打开的盒子的值在每一轮之后才显示给学习者。我们还将我们的结果推广到其他常用的潘多拉盒子和最小和集覆盖，涉及选择一个以上的值受到拟阵约束的研究变种。
英文摘要：
Two central problems in Stochastic Optimization are Min Sum Set Cover and Pandora's Box. In Pandora's Box, we are presented with $n$ boxes, each containing an unknown value and the goal is to open the boxes in some order to minimize the sum of the search cost and the smallest value found. Given a distribution of value vectors, we are asked to identify a near-optimal search order. Min Sum Set Cover corresponds to the case where values are either 0 or infinity. In this work, we study the case where the value vectors are not drawn from a distribution but are presented to a learner in an online fashion. We present a computationally efficient algorithm that is constant-competitive against the cost of the optimal search order. We extend our results to a bandit setting where only the values of the boxes opened are revealed to the learner after every round. We also generalize our results to other commonly studied variants of Pandora's Box and Min Sum Set Cover that involve selecting more than a single value subject to a matroid constraint.
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