A Framework for Probabilistic Decision-Making Using Change-of-Probability Measures
A Framework for Probabilistic Decision-Making Using Change-of-Probability Measures
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DOI：
10.1109/access.2020.3020928
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发表时间：
2020
期刊：
影响因子：
3.9
通讯作者：
S. Enayati;H. Pishro-Nik
中科院分区：
文献类型：
--
作者：
S. Enayati;H. Pishro-Nik
概率决策是从工程到社会科学的许多学科都要考虑的基本问题。在这篇文章中，我们将讨论在大数定律（LLN）不适用的情况下的决策。非LLN制度包括几乎所有高影响决策。人工智能（AI）决策的兴起进一步增加了为此类问题开发原则性方法的重要性。在这方面，我们首先介绍了一种称为有界期望（BE）的方法来应用忽略可忽略概率的公认原则。我们表明，BE提供了一些令人满意的结果和见解，一些决策问题。指出BE的一些缺点，然后我们转向一个更一般的设置，使用改变的概率措施。我们表明，所提出的方法可以被认为是一个推广的期望效用理论（EUT）从两个不同的角度。首先，随着重复次数的增加，该方法收敛于EUT。此外，当基本失真参数，$\$，设置为零，所提出的理论减少到EUT。然后，我们提出了一个系统的方法来应用开发的框架，非LLN的决定。最后，通过一个真实的例子，我们比较了所提出的方法和传统的方法所做的决定。据推测，由于非LLN制度下的决策的复杂性和多维性，所提出的想法可能会导致相当多的进一步研究，其中一些在本文中进行了讨论。
Probabilistic decision-making is a fundamental problem considered in many disciplines from engineering to social sciences. In this article, we address decision-making in contexts where the law of large numbers (LLN) does not apply. Non-LLN regimes include almost all high-impact decisions. The rise of artificial intelligence (AI) decision making is further increasing the importance of developing principled approaches for such problems. In this regard, we first introduce a method called bounded expectation (BE) to apply the accepted principle of ignoring negligible probabilities. We show that BE provides some satisfactory results and insights into some decision-making problems. Pointing out some shortcomings of BE, we then turn to a much more general setting, using change-of-probability measures. We show that the proposed approach can be considered a generalization of expected utility theory (EUT) from two different perspectives. First, the approach converges to EUT as the number of repetitions grows. Additionally, when the fundamental distortion parameter, $\epsilon $ , is set to zero, the proposed theory reduces to EUT. We then propose a systematic approach to applying the developed framework to non-LLN decisions. Finally, through a real-world example, we compare the decisions made with the proposed method and the conventional methods. It is speculated that due to the complexity and multidimensionality of decision-making under non-LLN regimes, the presented ideas can potentially lead to considerable further research, some of which is discussed in this article.