CAREER: Efficient Learning of Equilibria in Dynamic Bayesian Games with Nash, Bellman and Lyapunov

职业生涯：与纳什、贝尔曼和李亚普诺夫一起有效学习动态贝叶斯博弈中的均衡

• 批准号: 2238838
• 负责人: Lichun Li
• 金额: $ 50万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-05-01 至 2028-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2238838&HistoricalAwards=false
• 关键词: CAREER; Efficient; Learning; Equilibria; Dynamic

Dynamic Bayesian games characterize long-term interactions among multiple organizations or agents with private information that changes over time. The balance among the agents occurs when every agent has the best response to the others’ strategies. At this equilibrium, agents strategically exploit their private information to gain long-term benefits. Dynamic Bayesian games have broad applications in cyber, physical, economic, and social systems like cyber security, resource allocation, war field, market share, and governance of social media. The main difficulty in bringing the intelligence of the game into the society and the economy is the extremely high computational complexity of the equilibrium. Currently, only supercomputers can handle the computation. This project proposes an innovative method that integrates AI, control theory, and game theory to provide efficient computation algorithms such that the computation can be handled on typical PCs, which makes it possible to fight efficiently and intelligently against millions of cyber-attacks, to rapidly allocate resources in 6G ultra-dense networks in a near-optimal way, and to automate the governance of metaverse in real-time. The project will build an initial model of a support system for female engineers, including a freshman course to enhance female students’ interest in engineering and early research opportunities to encourage female students to pursue further engineering careers. Meanwhile, the project will regularly deliver the research results to the public using narratives in summer camps in cooperation with the Challenger Learning Center, STEM events, and open house events. This project aims at breaking the curse of time in Bayesian games and develop efficient algorithms to compute the perfect Bayesian equilibrium in long/infinite horizon stochastic Bayesian games with typical PCs. Computing equilibria in dynamic Bayesian games is extremely difficult. Current algorithms need to compute equilibrium for every possible information set. The total number of possible information sets grows exponentially with respect to time, and hence current algorithms soon exhaust computing resources. This project will break the curse of time through three innovative approaches. First, the Bellman equation in dynamic Bayesian games suggests that the current stage equilibrium can be computed based on the value function in the future, so evaluating the Nash equilibrium at all information sets is unnecessary. Second, Lyapunov-like energy functions established based on our prior work promise to solve the Bellman equation efficiently. Third, our proposed dual neural network structure has great potential for approximating the value function with time-insensitive structures without introducing the curse of dimensionality. This project will develop a video game to test the algorithms against humans in real-time. This algorithm has great potential to automate and intellectualize defense strategies in security problems, coordination strategies in multi-agent systems, resource allocation in 6G ultra-dense networks, governance of metaverse, and much more. As the algorithms can be run on typical PCs, it will allow many more scientists and researchers to investigate the complicated equilibrium behavior in general stochastic Bayesian games.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.

动态的贝叶斯游戏是多个组织或代理商之间具有私人信息随时间变化的私人信息的长期互动的特征。当每个代理商对他人的策略都有最佳反应时，代理之间的平衡发生。在这种同等的情况下，代理商从战略上利用其私人信息来获得长期利益。动态的贝叶斯游戏在网络，物理，经济和社会系统中具有广泛的应用，例如网络安全，资源分配，战场，市场份额和社交媒体治理。将游戏的智能带入社会和经济的主要困难是同等的计算复杂性。当前，只有超级计算机才能处理计算。该项目提出了一种创新方法，该方法集成了AI，控制理论和游戏理论，以提供有效的计算算法，以便可以在典型的PC上处理计算，这使得有可能在6G超密度网络中快速分配近距离的网络，并在实现近距离的情况下，并在实现近距离的情况下，并可以在6G超密度的网络中迅速分配，并在实现的实现中，并在实现近距离的情况下进行了自动分配。该项目将为女性工程师建立支持系统的初始模型，包括新生课程，以增强女学生对工程学和早期研究机会的兴趣，以鼓励女学生从事进一步的工程职业。同时，该项目通常会在夏令营中与挑战者学习中心，STEM事件和开放日活动合作，使用夏令营中的叙述向公众提供研究结果。该项目旨在打破贝叶斯游戏中的时间曲线，并开发有效的算法，以计算带有典型PC的长/无限地平线随机贝叶斯游戏中完美的贝叶斯平衡。动态贝叶斯游戏中的计算平衡非常困难。当前算法需要计算每个可能的信息集的平衡。可能的信息集总数相对于时间呈指数增长，因此当前的算法很快耗尽了计算资源。该项目将通过三种创新方法破坏时间的曲线。首先，动态贝叶斯游戏中的Bellman方程表明，可以根据将来的价值函数来计算当前阶段平衡，因此不需要在所有信息集中评估NASH平衡。其次，基于我们先前的工作承诺，建立了类似Lyapunov的能量功能，以有效地解决Bellman等效性。第三，我们提出的双重神经网络结构具有巨大的潜力，可以在不引入维度曲线的情况下与时间不敏感的结构近似值函数。该项目将开发一个视频游戏，以实时测试针对人类的算法。该算法具有巨大的潜力，可以在安全问题，多代理系统中的协调策略，6G超密集网络中的资源分配，元网络治理等自动化和知识化。由于可以在典型的PC上运行算法，因此它将允许更多的科学家和研究人员研究一般随机贝叶斯游戏中复杂的平衡行为。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来通过评估来诚实地支持。