Abstract : We propose a PDE framework for modeling the distribution shift of a strategic population interacting with a learning algorithm. We consider two particular settings one, where the objective of the algorithm and population are aligned, and two, where the algorithm and population have opposite goals. We present convergence analysis for both settings, including three different timescales for the opposing-goal objective dynamics. We illustrate how our framework can accurately model real-world data and show via synthetic examples how it captures sophisticated distribution changes which cannot be modeled with simpler methods.

Keywords : Distribution shift; coupled gradient flows; convergence to equilibrium