Breaking the ‘curse of dimensionality’ will take math, not magic

Engineering professor Hao Xu gets CAREER grant to enhance large-scale computerized systems.

Head shot of Assistant Professor Hao Xu

Breaking the ‘curse of dimensionality’ will take math, not magic

Engineering professor Hao Xu gets CAREER grant to enhance large-scale computerized systems.

Head shot of Assistant Professor Hao Xu

Complex computer systems such as 5G networks and smart transportation have the potential to transform the world, but electrical and biomedical engineering Assistant Professor Hao Xu sees a stumbling block.

Those large scale multi-agent systems (LS-MAS) require huge information exchanges between multiple, autonomous computerized systems that use game theory (the study of mathematical models of strategic interactions between computerized systems), artificial intelligence (AI) and machine learning (ML). And while game theory, AI and ML have been successfully applied to multi-agent systems, Xu says there still is a gap in applying those theories and techniques to LS-MAS.

That’s because the large number of agents in an LS-MAS will cause a difficult-to-solve computational complexity in the system’s optimization and learning: the curse of dimensionality. Xu will try to lift that curse in his research project “Toward a Hierarchical Game Theory and Hybrid Learning Framework for Safe and Efficient Large Scale Multi-Agent System.” Work began this month on the five-year project, funded by a $504,751 National Science Foundation CAREER award. CAREER awards are the NSF’s most prestigious awards in support of early-career faculty who have the potential to serve as academic role models and research and education, and to lead advances in the mission of their department or organization.

Here, Xu discusses his research:

What is the goal of your CAREER project?

Large scale multi-agent systems (LS-MAS), such as wide area power management systems, smart transportation, ultra-dense network in 5G/6G, and so on, are transforming our world rapidly. Before harvesting the benefits from those LS-MAS, it is necessary to develop a feasible methodology that can enhance the efficiency and resiliency of LS-MAS in real-time even under uncertainties and disturbances.

Although existing game theory, artificial intelligence (AI), and machine learning (ML) achievement in multi-agent systems optimization are exciting, there is still a gap for applying those theories and techniques to LS-MAS because a large number of agents will cause the intractable computational complexity in both optimization and learning, well-known as “curse-of-dimensionality.”

The goal of this CAREER project is to advance foundational knowledge of game theory and scientific methodologies of data-enabled learning for enhancing the resiliency and efficiency in LS-MAS. First, this project will develop a novel hierarchical game theory (HGT) to balance the optimal efficiency and computational complexity. Then, a new type of stochastic differential equation-based actor-critic reinforcement learning will be designed to solve the high dimensional HGT-based optimization problem. This CAREER project will lead a new direction in machine learning, optimal control and game theory in real-time LS-MAS optimization, and also contribute to a variety of emerging LS-MAS, e.g. smart transportation, wide area power management systems, etc., which are of national priority.

What potential impact can the project have on society? 

With the rapid development of the Internet of Things as well as big data related technologies, traditional small-scale multi-agent systems have been widely extended to large scale. However, recent advances in system optimization cannot be efficiently used on real LS-MAS due to the well-known “Curse of Dimensionality.” This CAREER project will tackle this challenge by not only building new theoretical foundations but also providing novel data-enabled learning technology that can fill the gap between theory and practical applications. Therefore, the successful completion of this research will provide these necessary components to facilitate the optimal design of LS-MAS and foster their adoption.

Moreover, if this project is successful, we could extend these results to other fields facing similar large dimensionality challenges. Examples include smart grids, the Internet of Things, 5G/6G communication, and smart transportation systems.

The project, if successful, also will lead to a significant economic impact. The proposed research can pave a way for applying cutting-edge Artificial Intelligence and Machine Learning (AI/ML) technology to real-time systems. It will make smart cities, smart transportation, and smart manufacturing truly smart.

Meanwhile, the outreach component of the educational program in this project will improve K-12, pre-college, and underrepresented students’ awareness of the potential and attractiveness of a research and engineering career. 

What impact will the research have in your discipline? 

This research will profoundly impact applied Artificial Intelligence and Machine Learning (AI/ML). After decades, there is still a long way for us to apply current AI/ML techniques into real-time systems (e.g. smart transportation, 5G/6G network, Robot-assisted advanced manufacturing system), due to two reasons:

  • Increasing AI/ML computational complexity while real-time systems are being more and more complicated
  • Lacking the effective mechanism to guarantee the system performance (e.g. stability, etc.) before learning is fully completed.

To enhance the practicality of AI/ML techniques, this research will build new theoretical foundations that can reduce the real-time system design complexity fundamentally. Moreover, this research will also provide a Quality-of-Performance (QoP) driven mechanism and integrate it with AI/ML techniques to ensure the system performance during learning. The success of this project will pave the way for applying advanced AI/ML technology to a variety of complex real-time systems. 

Last words… 

I am very honored to receive this prestigious award. It provides me and my team with strong support to carry out the proposed research and education agenda. With this award, we can further expand our lab and have more students work on the proposed topic of hierarchical game theory as well as hybrid learning techniques and further implement them into large scale multi-agent systems, e.g. robot-assisted advanced manufacturing systems, 5G/6G network, etc.

I would like to thank all my graduated and current students for their excellent research work and contribution to this project. I want to thank the Department of Electrical and Biomedical Engineering, the College of Engineering Research Office and Dean’s Office, Research & Innovation as well as University leadership for their support from the university level. Last but not least, I want to thank my family, friends, and collaborators without whose help I could not do this.

Students and future collaborators who are interested in this project and would like to participate can find more information at Assistant Professor Hao Xu's Pack Page or email Professor Xu

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