Cyber resilience is a complementary concept to cybersecurity, focusing on the preparation, response, and recovery from cyber threats that are challenging to prevent. Organizations increasingly face such threats in an evolving cyber threat landscape. Understanding and establishing foundations for cyber resilience provide a quantitative and systematic approach to cyber risk assessment, mitigation policy evaluation, and risk-informed defense design. A systems-scientific view toward cyber risks provides holistic and system-level solutions. This chapter starts with a systemic view toward cyber risks and presents the confluence of game theory, control theory, and learning theories, which are three major pillars for the design of cyber resilience mechanisms to counteract increasingly sophisticated and evolving threats in our networks and organizations. Game and control theoretic methods provide a set of modeling frameworks to capture the strategic and dynamic interactions between defenders and attackers. Control and learning frameworks together provide a feedback-driven mechanism that enables autonomous and adaptive responses to threats. Game and learning frameworks offer a data-driven approach to proactively reason about adversarial behaviors and resilient strategies. The confluence of the three lays the theoretical foundations for the analysis and design of cyber resilience. This chapter presents various theoretical paradigms, including dynamic asymmetric games, moving horizon control, conjectural learning, and meta-learning, as recent advances at the intersection. This chapter concludes with future directions and discussions of the role of neurosymbolic learning and the synergy between foundation models and game models in cyber resilience.

翻译：网络弹性是网络安全的补充性概念，聚焦于对难以预防的网络威胁的准备、响应与恢复。在不断演变的网络威胁格局中，各类组织日益面临此类威胁。理解并建立网络弹性基础，可为网络风险评估、缓解策略评估及风险驱动的防御设计提供定量化、系统化的方法。从系统科学视角审视网络风险，能够提供整体性的系统级解决方案。本章从网络风险的系统观出发，阐述博弈论、控制论与学习理论三大理论支柱的融合——这些理论是设计网络弹性机制以应对网络与组织中日益复杂和不断演变的威胁的核心工具。博弈论与控制论方法提供了捕捉防御方与攻击方之间战略动态交互的建模框架。控制与学习框架共同构成反馈驱动机制，支持对威胁的自主适应性响应。博弈与学习框架则提供数据驱动方法，能够主动推理对抗行为与弹性策略。三者融合为网络弹性分析与设计奠定了理论基础。本章重点介绍动态非对称博弈、移动时域控制、推测性学习与元学习等前沿交叉理论范式，最后探讨神经符号学习的作用，以及基础模型与博弈模型在网络弹性中的协同发展等未来方向。