单个隐藏目标的最优随机搜索
Optimal random search for a single hidden target
摘要：
单个目标隐藏在从预定概率分布中选择的位置处。然后，搜索器必须找到第二个概率分布，从该概率分布中对随机搜索点进行采样，以便在最少次数的尝试中找到目标。这里将表明，如果搜索者必须非常接近目标才能找到它，那么最佳搜索分布与目标分布的平方根成正比。对于高斯目标分布，最优搜索分布近似为高斯分布，其标准差与搜索者必须与目标的距离成反比。对于网络，搜索者随机采样节点并沿着边缘寻找固定目标，最优选择是以与出度的平方根加1成正比的概率采样节点，或者根本不采样。
英文摘要：
A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network, where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is to either sample a node with probability proportional to the square root of the out degree plus one or not at all.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
