Dominance functions cut data needs for monotone system safety

Existing data-driven safety analysis for unknown dynamical systems often demands massive datasets to yield rigorous guarantees, or resorts to heuristics with no formal proof. A new paper by Galarza-Jimenez, Zamani, and Jafarpour tackles this bottleneck by leveraging the structural property of monotonicity. The authors introduce dominance functions—certificates built directly from system trajectories, regardless of whether those trajectories were safe. These functions are dissipative (monotonically decreasing along any trajectory) and sufficiently expressive to characterize safety for any monotone system. This means that even a handful of observed trajectories can produce a formal safety certificate, eliminating the need for exhaustive data collection.

To operationalize their insight, the team develops an efficient sampling-based optimization framework that searches for safety certificates as linear combinations of dominance functions. The same approach works for both verification (is the system safe under a given controller?) and synthesis (design a controller that keeps the system safe). They validate the method on two monotone systems, successfully deriving safety certificates from a small number of trajectories. The work opens the door to data-efficient formal safety guarantees for cyber-physical systems where monotonicity is common—such as biological networks, power grids, and temperature regulation—making it a practical tool for real-world AI control deployment.