$Γ$ -maximin、$Γ$ -maximax和区间优势算法的改进和基准测试
Improving and benchmarking of algorithms for $Γ$-maximin, $Γ$-maximax and interval dominance
摘要：
$Γ$ -maximin、$Γ$ -maximax和区间优势是在严重不确定性情况下，当概率分布只能部分确定时进行决策的常见决策准则。人们可以通过求解线性规划序列来应用这三个准则。在这项研究中，我们提出了新的算法，这些标准和现有的标准算法的性能进行比较。具体来说，我们使用有效的方法，在以前的工作的基础上，找到这些算法的共同的初始可行点。利用这些初始可行点，我们开发早期停止标准，以确定赌博是否是$Γ$ -maximin，$Γ$ -maximax或区间显性。我们观察到，原始-对偶内点方法从这些改进中受益匪浅。在我们的模拟中，我们发现，我们提出的算法优于标准算法时，较低的预测域的大小是小于或等于决策和结果的大小。然而，我们提出的算法不优于标准算法的情况下，较低的预测域的大小是远远大于的大小的决定和结果。
英文摘要：
$Γ$-maximin, $Γ$-maximax and inteval dominance are familiar decision criteria for making decisions under severe uncertainty, when probability distributions can only be partially identified. One can apply these three criteria by solving sequences of linear programs. In this study, we present new algorithms for these criteria and compare their performance to existing standard algorithms. Specifically, we use efficient ways, based on previous work, to find common initial feasible points for these algorithms. Exploiting these initial feasible points, we develop early stopping criteria to determine whether gambles are either $Γ$-maximin, $Γ$-maximax or interval dominant. We observe that the primal-dual interior point method benefits considerably from these improvements. In our simulation, we find that our proposed algorithms outperform the standard algorithms when the size of the domain of lower previsions is less or equal to the sizes of decisions and outcomes. However, our proposed algorithms do not outperform the standard algorithms in the case that the size of the domain of lower previsions is much larger than the sizes of decisions and outcomes.
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。
