A team led by Johns Hopkins researchers has created a mathematical model that explores how humans make decisions when they are unsure about outcomes. The model also provides a structured way to determine how cautious someone should be when making decisions under uncertain conditions, leading to more efficient choices. The model can also be used as a tool to figure out how comfortable others are with taking risks.

“The model and the accompanying research provide a structured way to determine the appropriate level of conservativeness in decision-making, leading to more efficient decisions under uncertainty,” said Zhirui Liang, ENGR ’25 (PhD), who led the project with Qi Li, a master’s candidate in the Whiting School of Engineering’s Department of Applied Mathematics and Statistics. “It also offers us a tool to infer others’ risk preferences.”

The approach combines distributionally robust optimization (DRO)—a mathematical framework that enables decision-makers to optimize solutions that perform well under the worst-case scenario—with inverse optimization (IO)—a data-driven technique that uncovers hidden information in a decision-making process—to form an inverse DRO (I-DRO) model. This new model allows the researchers to analyze how people make decisions under uncertainty, evaluate their risk preferences, and understand the reasoning behind their decisions.

Zhirui Liang presenting the research at the 2025 ROSEI Summit

The team’s work is described in papers in the Proceedings of the 63rd IEEE Conference on Decision and Control, IEEE Control Systems Letter, and the Proceedings of the 59th Annual Conference on Information Science and Engineering (CISS), as well as a poster that won Liang the best poster award at the 2025 Grid Science Winter School and Conference at Los Alamos National Laboratory.

Though the researchers designed the model for use in various fields, they applied it to understanding the conservativeness of independent system operators (ISOs)—professionals who control the operation of power generators to meet electricity demand while ensuring the reliability and economic efficiency of power systems. ISOs must make decisions under uncertainty, particularly regarding the variability of renewable energy sources.

“Finding the optimal conservativeness level is important for ISOs because even small changes can lead to large variations to the total operational cost of a power system,” Liang said. “If an ISO is more conservative—meaning they anticipate greater uncertainty in the renewable power generation—they may schedule additional flexibility from costly controllable resources, such as energy storage, in the day ahead market, in which electricity is bought and sold one day before delivery. However, if the conservativeness level is too high, they risk unnecessarily increasing costs over time.”

The group aimed to answer two questions: What is the optimal level of conservativeness given the available information, and how should the conservativeness level be adjusted as more information becomes available? Their study showed that the optimal conservativeness level depends on how well decision-makers can quantify uncertainty.

“The idea is simple – if a decision turns out to be too conservative, you naturally adjust your future decisions based on the outcome,” Liang said. “Our mathematical model quantifies this reasoning process and helps decision-makers find and reach the optimal conservativeness level more efficiently.”

Additionally, the group looked at whether you can infer another decision-maker’s conservativeness based on their past decisions.

“The I-DRO model can reveal a person’s conservativeness by analyzing their past decisions under various environmental factors,” Liang said. “By tracking a person’s decision patterns over time, we can predict their future behavior. This is particularly valuable for electricity market participants, as it enables them to design more profitable strategies in response to other market players.”

Liang, now a postdoctoral researcher and member of the Center for Energy, Environmental and Economic Systems Analysis at Argonne National Laboratory, plans to continue this work, exploring the economic value of knowing a decision-maker’s conservativeness level, as well as how the electricity market-clearing results might change and how the market structure should be adapted if a significant number of market participants were using the team’s model or a similar tool.

“Finding answers to those questions could have big implications for the future electricity markets, where artificial intelligent (AI) and data-driven methods are becoming increasing prevalent,” Liang said.

The research team was supervised by Yury Dvorkin, an associate professor in the Whiting School of Engineering’s Department of Electrical and Computer Engineering and Department of Civil and Systems Engineering, as well as a core member of the Ralph O’Connor Sustainable Energy Institute (ROSEI). Other collaborators included Joshua Comden and Andrey Bernstein from the National Renewable Energy Laboratory.