In this paper, we address the computational feasibility of the class of decision theoretic models referred to as adversarial risk analyses (ARAs). These are models where a decision must be made with consideration for how an intelligent adversary may behave and where the decision-making process of the adversary is unknown and is elicited by analyzing the adversary's decision problem using priors on his utility function and beliefs. The motivation of this research was to develop a computational algorithm that can be applied across a broad range of ARA models; to the best of our knowledge, no such algorithm currently exists. Using a two-person sequential model, we incrementally increase the size of the model and develop a simulation-based approximation of the true optimum where an exact solution is computationally impractical. In particular, we begin with a relatively large decision space by considering a theoretically continuous space that must be discretized. Then, we incrementally increase the number of strategic objectives, which causes the decision space to grow exponentially. The problem is exacerbated by the presence of an intelligent adversary who also must solve an exponentially large decision problem according to some unknown decision-making process. Nevertheless, using a stylized example that can be solved analytically, we show that our algorithm not only solves large ARA models quickly but also accurately selects to the true optimal solution. Furthermore, the algorithm is sufficiently general that it can be applied to any ARA model with a large, yet finite, decision space.

中文翻译：

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多元对抗风险分析模型中的计算效率

在本文中，我们讨论了称为对抗风险分析（ARAs）的决策理论模型类别的计算可行性。在这些模型中，必须做出决策，要考虑到智能对手的行为方式，以及该对手的决策过程是未知的，并且是通过使用先验者的效用函数和信念来分析其决策问题而得出的。这项研究的动机是开发一种可应用于广泛的ARA模型的计算算法。据我们所知，目前尚无此类算法。使用两人顺序模型，我们逐步增加了模型的大小，并开发了基于模拟的真实最佳逼近，其中精确的解决方案在计算上不切实际。特别是，我们从一个相对较大的决策空间入手，首先考虑必须离散化的理论上连续的空间。然后，我们逐渐增加了战略目标的数量，这导致决策空间呈指数增长。聪明的对手的存在加剧了这个问题，对手也必须根据一些未知的决策过程来解决指数级的决策问题。然而，使用可以解析地求解的风格化示例，我们证明了我们的算法不仅可以快速求解大型ARA模型，而且可以准确地选择出真正的最优解。此外，该算法具有足够的通用性，可以应用于具有较大但有限的决策空间的任何ARA模型。