Algorithms for Computing with Uncertainty: Theory and Experiments

在做出决定之前，我们应该收集多少信息？这个问题是具有可解释不确定性的计算研究领域的基础。例如，假设我们要建立一个连接一组分支办公室的网络。对于分支机构的任意两个位置A和B，我们可以根据它们之间的距离估计在A和B之间建立链路的成本。在A和B之间建立链路的确切成本可以通过进一步的调查来确定，但这些调查需要时间和金钱。如果我们知道每对位置的确切链路成本，我们就可以使用已知的“最小生成树”问题算法来确定构建网络的最便宜方法。然而，首先确定所有位置对在它们之间建立链接的确切成本的方法是没有效率的：确定所有确切的链接成本将花费很长时间，并且获得该信息的成本将是显著的。因此，希望找到有效的方法，用于以巧妙的方式选择需要确定链路成本的位置对，同时仍然实现能够利用所获得的信息构建廉价网络的目标。具有可探索不确定性的计算算法解决了这样的问题：它们指定了一种策略，用于选择应该确定确切信息的位置对，直到获得足够的信息来确定要构建的最佳可能网络。更一般地说，具有可解释不确定性的计算处理部分输入不确定的问题以前的不确定性计算工作主要集中在一个接一个顺序查询的设置上（这可能需要很长时间），并且目标是在确保获得足够的信息以最佳地解决问题的同时进行尽可能少的查询。这就留下了一个问题，即如果可以同时并行地进行多个查询，则应该如何选择查询，这在许多应用中是现实的（例如，在上面概述的应用中，可以并行地确定在几对分支办公室位置之间建立链路的确切成本）。尚未充分考虑的另一个方向是目标是优化查询成本和最终确定的解决方案的成本的组合的设置。该项目旨在通过解决这些开放性问题并开发可证明在所描述的场景中工作良好的新算法，将具有可探索不确定性的计算研究提升到一个新的水平。在项目中开发的方法可能是有用的任何决策的情况下，额外的信息输入数据的问题是在原则上是可用的，可以获得成本。

How much information should we collect before making a decision? This question underlies the research area of computing with explorable uncertainty. For example, assume that we want to build a network connecting a set of branch offices. For any two locations A and B of branch offices, we have an estimate of the cost for building a link between A and B based on the distance between them. The exact cost of building a link between A and B can be determined by further investigations, but these investigations take time and cost money. If we knew the exact link cost for every pair of locations, we could determine the cheapest way of building the network using a known algorithm for the "minimum spanning tree" problem. The approach of first determining for all pairs of locations the exact cost of building a link between them is not efficient, however: It will take a long time to determine all the exact link costs, and the costs for obtaining that information will be significant. It is therefore desirable to find efficient methods for selecting in a clever way the pairs of locations for which the link costs need to be determined, while still achieving the goal of being able to build a cheap network with the information gained. Algorithms for computing with explorable uncertainty solve such problems: They specify a strategy for selecting the pairs of locations for which exact information should be determined until sufficient information has been gained to determine the best possible network to be built. More generally, computing with explorable uncertainty deals with problems where part of the input is uncertain (known only approximately) but can be obtained at a cost using a query operation.Previous work on computing with uncertainty has focused on the setting where queries are made one by one sequentially (which may take a long time) and where the goal is to make as few queries as possible while ensuring that sufficient information is obtained to solve the problem optimally. This leaves open the question of how the queries should be selected if a number of queries can be made at the same time in parallel, which is realistic in many applications (for example, in the application outlines above, the exact costs of building links between several pairs of branch office locations could be determined in parallel). Another direction that has not yet been sufficiently considered is the setting where the goal is to optimize a combination of the query cost and the cost of the solution determine in the end. The project aims to take research in computing with explorable uncertainty to the next level by addressing these open questions and developing new algorithms that work provably well in the described scenarios. Methods developed in the project can potentially be useful to any decision-making scenarios where additional information about the input data of a problem is available in principle and can be obtained at a cost.