In this paper we address the computational feasibility of the class of decision theoretic models referred to as adversarial risk analyses (ARA). 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.
翻译:在本文中,我们讨论了称为对抗性风险分析(ARA)的决定理论模型的计算可行性。这些模型是必须作出决定的模型,其中必须考虑智能对手的行为方式和对手的决策过程未知,并且通过使用其实用功能和信念的先验方法分析对手的抉择问题而得出。研究的动机是开发一种计算算法,可以适用于广泛的ARA模型;据我们所知,目前没有这种算法。使用两人相继模型,我们逐步增加模型的规模,并在精确的解决方案在计算上不切实际的情况下,对真正的最佳方法进行模拟近似。特别是,我们从一个相对大的决策空间开始,先考虑一个必须分解的理论连续性空间。然后,我们逐渐增加导致决策空间急剧增长的战略目标的数量。由于存在智能的对称,他们也必须根据一些未知的决策过程解决一个指数性巨大的决策问题。然而,我们使用一个基于模型的模拟模型,可以快速地模拟真实地近似最优的近似性模拟,我们只能以分析性的方式展示我们的最佳算法。