CAREER: Catastrophic Rare Events: Theory of Heavy Tails and Applications

这项学院早期职业发展计划(Career)赠款将通过开发数学工具来帮助促进国家繁荣和福利，这些工具提供了战略，以了解和减轻与“重尾”现象相关的风险。重尾分布为看似不同的罕见事件提供了有用的数学模型，例如全球大流行、2012年印度大停电和2007年金融危机。除了这种孤立的灾难性事件，重尾现象在大规模复杂系统和现代算法中普遍存在。重尾巴的一种特别简单和众所周知的表现是所谓的“80-20规则”，它的变体在广泛的应用领域中反复被发现。在存在重尾的情况下，高影响的罕见事件最终肯定会发生，而且可能比决策者可能考虑的更频繁。考虑(甚至利用)这种罕见事件造成的影响，将支持在许多重要情况下设计和运行可靠和有弹性的系统，包括环境灾难、电力系统故障、金融危机。随之而来的教育计划旨在扩大STEM对代表性不足社区的兴趣，并通过让他们掌握风险分析的基本技能来培养未来的学术界、工业界和政府领导人。这项研究将发展一种关于重尾随机系统的大偏差和亚稳定的全面理论。经典的大偏差和稀有事件模拟理论有很长的历史，但当潜在的不确定性是重尾的时候，这些方法和亚稳态框架往往是不足的。该项目利用并扩展了极值理论、优化、控制和随机模拟方面的最新进展，通过构建为重尾系统量身定做的大偏差和亚稳定框架来填补这一空白。有了新的框架，该项目还将解决人工智能和精算科学中的公开问题。这项研究将有助于为设计可靠和负责任的人工智能奠定严格的理论基础，以便该技术可以应用于高风险的决策问题。成功实施这样的计划将扩大我们对许多随机系统中系统故障和相变是如何产生的理解，这反过来将为保险风险管理和负责任的人工智能设计提供被证明有效的计算机械。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This Faculty Early Career Development Program (CAREER) grant will contribute to the advancement of national prosperity and welfare by developing mathematical tools that provide strategies to understand and mitigate risk associated with the "heavy-tail" phenomena. Heavy-tailed distributions provide useful mathematical models for seemingly disparate rare events, such as the global pandemic, the 2012 blackout in India, and the 2007 financial crisis. Beyond such isolated catastrophic events, heavy tails are pervasive in large-scale complex systems and modern algorithms. A particularly simple and well-known manifestation of heavy tails is the so-called “80-20 rule”, whose variations are repeatedly discovered in a wide variety of application areas. Under the presence of heavy tails, high-impact rare events are guaranteed to happen eventually, and may occur more frequently than decision-makers may account for. Accounting for (or even utilizing) the impact inflicted by such rare events will support the design and operation of reliable and resilient systems in many important scenarios, including environmental catastrophes, power system failures, financial crises. The accompanying educational plan aims to broaden STEM interest in underrepresented communities and train future leaders of academia, industry, and government by equipping them with fundamental skills in risk analysis.This research will develop a comprehensive theory of large deviations and metastability for heavy-tailed stochastic systems. The classical theory of large deviations and rare-event simulation has a long history but these approaches and the metastability framework often fall short when the underlying uncertainties are heavy-tailed. This project leverages and extends recent advances in extreme value theory, optimization, control, and stochastic simulation to fill the gap by building large deviations and metastability frameworks tailored for heavy-tailed systems. With the new framework, the project will also address open problems in artificial intelligence and actuarial science. This research will contribute to a rigorous theoretical foundation for designing reliable and accountable AI so that the technology can be applied to high-stake decision-making problems. Successful implementation of such a program will expand our understanding of how system failures and phase transitions arise in many stochastic systems, which, in turn, will provide provably efficient computational machinery for insurance risk management and accountable AI design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.