Abstract
We study automated intrusion response for an IT infrastructure and formulate the interaction between an attacker and a defender as a partially observed stochastic game. To solve the game we follow an approach where attack and defense strategies co-evolve through reinforcement learning and self-play toward an equilibrium. Solutions proposed in previous work prove the feasibility of this approach for small infrastructures but do not scale to realistic scenarios due to the exponential growth in computational complexity with the infrastructure size. We address this problem by introducing a method that recursively decomposes the game into subgames with low computational complexity which can be solved in parallel. Applying optimal stopping theory we show that the best response strategies in these subgames exhibit threshold structures, which allows us to compute them efficiently. To solve the decomposed game we introduce an algorithm called Decompositional Fictitious Self-Play (dfsp), which learns Nash equilibria through stochastic approximation. We evaluate the learned strategies in an emulation environment where real intrusions and response actions can be executed. The results show that the learned strategies approximate an equilibrium and that dfsp significantly outperforms a state-of-the-art algorithm for a realistic infrastructure configuration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Alpcan, T., Basar, T.: Network Security: A Decision and Game-Theoretic Approach, 1st edn. Cambridge University Press, Cambridge (2010)
Altman, E., et al.: Jamming game with incomplete information about the jammer. In: Conference on Performance Evaluation Methodologies and Tools (2009)
Bellman, R.: A Markovian decision process. J. Math. Mech. 6(5), 679–684 (1957)
Brooks, R.: A robust layered control system for a mobile robot. IEEE J. Robot. Autom. 2(1), 14–23 (1986)
Brown, G.W.: Iterative solution of games by fictitious play. In: Activity Analysis of Production and Allocation, pp. 374–376 (1951)
Cormen, T., et al.: Introduction to Algorithms, 4th edn. The MIT Press, Cambridge (2022)
Hammar, K., Stadler, R.: Finding effective security strategies through reinforcement learning and self-play. In: International Conference on Network and Service Management (CNSM 2020), Izmir, Turkey (2020)
Hammar, K., Stadler, R.: Learning intrusion prevention policies through optimal stopping. In: International Conference on Network and Service Management (CNSM 2021), Izmir, Turkey (2021). https://arxiv.org/pdf/2106.07160.pdf
Hammar, K., Stadler, R.: Intrusion prevention through optimal stopping. IEEE Trans. Netw. Serv. Manag. 19(3), 2333–2348 (2022)
Hammar, K., Stadler, R.: Learning near-optimal intrusion responses against dynamic attackers. IEEE Trans. Netw. Serv. Manag. 1 (2023). https://doi.org/10.1109/TNSM.2023.3293413
Hammar, K., Stadler, R.: Scalable learning of intrusion responses through recursive decomposition (2023). https://arxiv.org/abs/2309.03292
Han, Y., et al.: Reinforcement learning for autonomous defence in software-defined networking. In: Bushnell, L., Poovendran, R., Başar, T. (eds.) GameSec 2018. LNCS, vol. 11199, pp. 145–165. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01554-1_9
Heinrich, J., Silver, D.: Deep reinforcement learning from self-play in imperfect-information games (2016). https://arxiv.org/abs/1603.01121
Hespanha, J., Prandini, M.: Nash equilibria in partial-information games on Markov chains. In: IEEE Conference on Decision and Control (2001)
Horák, K.: Scalable algorithms for solving stochastic games with limited partial observability. Ph.D. thesis, Czech Technical University in Prague (2019)
Horák, K., Bošanský, B.: Solving partially observable stochastic games with public observations. In: Proceedings of the AAAI Conference on Artificial Intelligence (2019)
Huang, L., Chen, J., Zhu, Q.: Factored Markov game theory for secure interdependent infrastructure networks. In: Rass, S., Schauer, S. (eds.) Game Theory for Security and Risk Management. SDGTFA, pp. 99–126. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75268-6_5
Huang, Y., Huang, L., Zhu, Q.: Reinforcement learning for feedback-enabled cyber resilience. Ann. Rev. Control 53, 273–295 (2022)
Kamhoua, C., et al.: Game Theory and Machine Learning for Cyber Security. Wiley, Hoboken (2021)
Kearns, M., Littman, M., Singh, S.: Graphical models for game theory. In: Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI 2001) (2001)
Krishnamurthy, V.: Partially Observed Markov Decision Processes: From Filtering to Controlled Sensing (2016). https://doi.org/10.1017/CBO9781316471104
Nair, R., et al.: Networked distributed POMDPs: a synthesis of distributed constraint optimization and POMDPs. In: Conference on Artificial Intelligence and the Innovative Applications of Artificial Intelligence (2005)
Nash, J.F.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)
Ouyang, Y., Tavafoghi, H., Teneketzis, D.: Dynamic games with asymmetric information: common information based perfect Bayesian equilibria and sequential decomposition. IEEE Trans. Autom. Control 62(1), 222–237 (2017)
Rasouli, M., Miehling, E., Teneketzis, D.: A scalable decomposition method for the dynamic defense of cyber networks. In: Rass, S., Schauer, S. (eds.) Game Theory for Security and Risk Management. SDGTFA, pp. 75–98. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75268-6_4
Schulman, J., et al.: Proximal policy optimization algorithms (2017). https://arxiv.org/abs/1707.06347
Seuken, S., Zilberstein, S.: Formal models and algorithms for decentralized decision making under uncertainty. Auton. Agents Multi-Agent Syst. 17, 190–250 (2008). https://doi.org/10.1007/s10458-007-9026-5
Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge (2009)
Siljak, D.: Large-Scale Dynamic Systems: Stability and Structure. Dover (1978)
Tambe, M.: Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned, 1st edn. Cambridge University Press, Cambridge (2011)
Timbers, F., et al.: Approximate exploitability: learning a best response in large games (2020). https://arxiv.org/abs/2004.09677
Topkis, D.M.: Minimizing a submodular function on a lattice. Oper. Res. 26(2), 305–321 (1978). https://www.jstor.org/stable/169636
Tsemogne, O., Hayel, Y., Kamhoua, C., Deugoué, G.: Optimizing intrusion detection systems placement against network virus spreading using a partially observable stochastic minimum-threat path game. In: Fang, F., Xu, H., Hayel, Y. (eds.) GameSec 2022. LNCS, vol. 13727, pp. 274–296. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-26369-9_14
Zan, X., et al.: A hierarchical and factored POMDP based automated intrusion response framework. In: Conference on Software Technology and Engineering (2010)
Zheng, J., Castañón, D.A.: Decomposition techniques for Markov zero-sum games with nested information. In: 52nd IEEE Conference on Decision and Control (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Hammar, K., Stadler, R. (2023). Scalable Learning of Intrusion Response Through Recursive Decomposition. In: Fu, J., Kroupa, T., Hayel, Y. (eds) Decision and Game Theory for Security. GameSec 2023. Lecture Notes in Computer Science, vol 14167. Springer, Cham. https://doi.org/10.1007/978-3-031-50670-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-50670-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-50669-7
Online ISBN: 978-3-031-50670-3
eBook Packages: Computer ScienceComputer Science (R0)