Q&A: Solving problems in big data with Serhat Aybat

UNIVERSITY PARK, Pa. — Big data has enabled numerous benefits for industries like health care, finance, consumer technology, insurance and cybersecurity. However, working with larger and larger datasets also increases numerical issues within the algorithms. To better understand these machine learning problems and design more efficient solutions, Necdet Serhat Aybat, associate professor of industrial engineering in the Penn State College of Engineering and expert on algorithms, will co-lead a three-year, $800,000 grant from the Office of Naval Research with co-principal investigator Mert Gürbüzbalaban, associate professor of management science and information systems at Rutgers University. 

In this Q&A with Penn State News, Aybat discussed the new project, titled “Primal-Dual Algorithms for Minimax Problems with Applications to Distributionally Robust Learning.” 

Q: What is a specific example of a minimax problem that arises in big data?  

Aybat: A minimax problem is a type of optimization problem where one party tries to minimize a value while another tries to maximize it. The objective is to find a balance or equilibrium point, often called a saddle point, where neither side can improve their position further without worsening the other’s. Minimax problems help solve real-world challenges in fairness, robustness and efficiency, all of which are critical in managing and learning from massive datasets in the big data era. 

Minimax problems arise for several reasons, including from machine learning and AI, when one model tries to create realistic data while another tries to distinguish fake data from real data. This setup naturally forms a minimax problem. 

Other systems, like cloud computing or network traffic systems, involve competing objectives: minimizing costs while maximizing efficiency or fairness. These trade-offs often translate into minimax formulations. 

Q: What are the goals of the project, and what would constitute success? 

Aybat: To tackle large-scale problems that plague modern data science, we often use a specific class of algorithms called the “stochastic first-order” methods. In this project, we focus on large-scale minimax problems and study a particular class of methods for solving them, called “stochastic first-order primal-dual methods.” These methods are fast and can handle big datasets well but have several problems. First, they may lead to unpredictable results: For example, some algorithms give solutions that are good on average, but individual results might be way off target. Second, current methods struggle with more complex problems arising in practice. Finally, their tuning is tricky; indeed, many algorithms need precise knowledge of certain mathematical properties, like “Lipschitz constants,” to adjust their steps efficiently. When these values are not available, the algorithms might take small, cautious steps, making them slower in practice. 

To address these issues, this project proposes to develop a smarter way to adjust step sizes automatically, using the local structure of the problem for better efficiency. We also will develop methods that ensure the output solution is reliable, not just on average but with a high probability of being close to the desired result. Finally, we will develop algorithms that can handle more complex problem types. 

If successful, this work could improve how we solve large, complex minimax problems, making tools like machine learning more robust and efficient for real-world applications. 

Q: How will this project apply to the real world?  

Aybat: This project addresses critical challenges in modern data-driven and optimization tasks, particularly those involving uncertainty, robustness and scalability. For example, the project’s advancements in solving minimax problems will help design robust AI systems that work well in the presence of unexpected variations, such as in health care, finance or cybersecurity.  

Systems like supply chains or autonomous vehicles, on the other hand, need to account for worst-case scenarios, and existing algorithms are either too slow or too limited in scope. By improving methods to handle non-smooth and non-convex minimax problems, which arise in deep learning, the project will lead to faster and more efficient solutions for robust systems, benefiting industries like transportation, logistics and renewable energy management. 

Additionally, this project’s novel algorithms will make deep learning models faster and more generalizable, impacting areas like natural language processing, computer vision and personalized recommendation systems. By focusing on time-varying and online problems, the project will also enhance real-time decision-making systems, such as autonomous drones, dynamic pricing platforms, or smart cities that are relevant for financial trading or monitoring system networks.  

Finally, the project’s improved algorithms will speed up computations in fields like bioinformatics, weather modeling or financial portfolio optimization. 

Q: Who are your collaborators at Penn State and Rutgers and what strengths do they bring to the project?   

Aybat: In addition to myself and Dr. Gürbüzbalaban, one Penn State graduate student and one Rutgers graduate student will be supported through the ONR award.  

I have expertise in continuous optimization with a focus on constrained optimization techniques and algorithmic analysis, while Dr. Gürbüzbalaban has extensive expertise in continuous optimization, incremental and online optimization, stochastic algorithms, applied stochastic analysis and machine learning.  

The research agenda of this new grant is a result of my previous grant from ONR on designing efficient methods for saddle point problems, which arise frequently in many key settings in today’s big data world.  

In the recently expired ONR grant, we investigated a problem with a specific structure, making it easier to solve. In this project, we generalize these ideas to a broader context that emerges in today’s complex data challenges. Specifically, we consider more general minimax problems that are common in modern fields like machine learning and resource optimization. They involve finding the best solution that balances competing objectives, such as creating a predictive model that is robust to errors or uncertainties in data.