Security Games on Series-Parallel Attack Graphs with Adaptive Attackers

2026-08-21

AI Summary

研究了在串联并联攻击图上，通过使用扩展的Gittins指数策略来对抗自适应攻击者的问题，提出了一种有效计算防御资源分配的方法。

Abstract

We study security games on attack graphs, where an adaptive attacker seeks to reach a target by sequentially attempting stochastic controls along the current attack frontier, while a defender allocates limited resources across controls to delay compromise. The attacker may choose among exponentially many attack routes and freely pivot between them as successes and failures are observed, yielding an exponentially large space of contingent attack policies. For any fixed defender allocation, we show that an optimal attacker policy on a two-terminal series-parallel attack graph is an index policy: at each step, the attacker selects an available control with the largest value of an extension of the classical Gittins index. The indices and the resulting attacker best response can be computed in polynomial time, without explicitly enumerating attack paths or contingent policies. To the best of our knowledge, this is the first optimal index characterization for adaptive attackers in security games on general series-parallel attack graphs. We further develop efficient algorithms for computing the attacker's exact utility and an exact defender subgradient, enabling deterministic first-order optimization of defensive resource allocations without sampling attack trajectories. Our framework strictly generalizes prior approaches restricted to parallel chains and out-trees, while exploiting the compositional structure of series-parallel graphs to support interpretable attacker policies and parallel computation across independent subgraphs. Experiments demonstrate that the resulting methods scale substantially better than naive explicit-state approaches while producing effective defensive allocations.

Problem

• Security Games
• Adaptive Attackers
• Attack Graphs
• Resource Allocation

Innovation

• index policy
• Gittins index
• series-parallel attack graphs
• polynomial time computation
• first-order optimization