PREDICTING THE BEHAVIOR OF AI AGENTS USING TRANSFER OPERATORS
Keywords: stochastic differential equations, markov process, operator theory
TL;DR: We predict the behavior of AI agents by studying the evolution of probability densities of their states.
Abstract: 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 stochastic nonlinear dynamical systems and adopting a probabilistic perspective to predict their statistical behavior using the Fokker-Planck equation. We formulate the approximation of the density transfer operator as an entropy minimization problem, which can be solved by leveraging the Markovian property and decomposing its spectrum. Our data-driven methodology simultaneously approximates the Markov 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.
Supplementary Material: zip
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 12209
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