A mathematical model developed by Haoyang Cao could help businesses, financial planners, and engineers make smarter high-stakes decisions.
Cao, an assistant professor of applied mathematics and statistics and a member of the Data Science and AI Institute, and her team focused on “impulse control” decision-making, a framework that reflects how organizations actually operate.
Rather than making tiny, continual changes, companies typically wait until conditions reach a tipping point and then act decisively.
“Our model is much closer to this reality,” Cao says. “People observe a situation over time, and only when the tipping point is reached, they make a move,” she adds, citing examples such as an Amazon warehouse suddenly placing a large restocking order or an investor moving funds in one major trade. “It’s sudden, not gradual. Real decision-making is messy,” she adds, “and algorithms must embrace that mess.”
That realism matters. Poorly timed decisions can lead to empty shelves, wasted inventory, unnecessary transaction fees, or lost profits. Yet translating those reactionary choices into mathematics has long challenged researchers. Current methods assume smooth, continuous behavior—but in the real world, decisions often arrive as abrupt shocks.
“People observe a situation over time, and only when the tipping point is reached, they make a move.” — Haoyang Cao
To bridge that gap, the team used reinforcement learning, where an algorithm learns through exploration and feedback, and built an operator-based framework that tracks how a system “renews” after each jump—for example, how inventory levels reset after a major order.
Rather than rely on simple rules and idealized equations, their flexible approach learns from experience to discover better timing and order sizes, identifying what “too low” means amid shifting demand, prices, and shipping costs.
The researchers are now expanding the work beyond a single decision-maker to situations where many agents interact, such as competing firms ordering from the same supplier or investors reacting to one another’s trades.
— SALENA FITZGERALD