Predicting AI Agent Behavior through Approximation of the Perron-Frobenius Operator

Predicting the behavior of AI-driven agents is particularly challenging without a preexisting model. In our paper, we address this by treating AI agents as nonlinear dynamical systems and adopting a probabilistic perspective to predict their statistical behavior using the Perron-Frobenius (PF) operator. We formulate the approximation of the PF operator as an entropy minimization problem, which can be solved by leveraging the Markovian property of the operator and decomposing its spectrum. Our data-driven methodology simultaneously approximates the PF operator to perform prediction of the evolution of the agents and also predicts the terminal probability density of AI agents, such as robotic systems and generative models. We demonstrate the effectiveness of our prediction model through extensive experiments on practical systems driven by AI algorithms.