解决Stackelberg网络对有限理性成瘾者的阻断
Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary
摘要：
这项工作研究了Stackelberg网络阻断游戏-一类重要的游戏，其中防御者首先将（随机）防御资源分配给图上的一组关键节点，而对手相应地选择其攻击这些节点的路径。我们考虑一个有限理性的对手，对手的反应模型是基于一个动态形式的经典的基于logit的离散选择模型。我们证明了在理性环境下为防守者寻找最优拦截策略的问题是NP难的。由此产生的优化实际上是非凸的，并且另外，涉及在指数级许多路径上求和的复杂项。我们解决这些计算挑战，提出了新的有效的近似算法有界的解决方案的保证。首先，我们提出了一个多项式时间的动态规划为基础的配方，以解决指数多路径的挑战。然后，我们证明了非凸目标的梯度也可以在多项式时间内计算，这使我们能够使用基于梯度的方法来有效地解决问题。其次，我们确定了一个受限制的问题，是凸的，因此基于梯度的方法找到这个受限制的问题的全局最优解。我们进一步确定温和的条件下，这个限制问题提供了一个有界的近似原问题。
英文摘要：
This work studies Stackelberg network interdiction games -- an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack these nodes accordingly. We consider a boundedly rational adversary in which the adversary's response model is based on a dynamic form of classic logit-based discrete choice models. We show that the problem of finding an optimal interdiction strategy for the defender in the rational setting is NP-hard. The resulting optimization is in fact non-convex and additionally, involves complex terms that sum over exponentially many paths. We tackle these computational challenges by presenting new efficient approximation algorithms with bounded solution guarantees. First, we address the exponentially-many-path challenge by proposing a polynomial-time dynamic programming-based formulation. We then show that the gradient of the non-convex objective can also be computed in polynomial time, which allows us to use a gradient-based method to solve the problem efficiently. Second, we identify a restricted problem that is convex and hence gradient-based methods find the global optimal solution for this restricted problem. We further identify mild conditions under which this restricted problem provides a bounded approximation for the original problem.
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