The Decoupled Risk Landscape in Performative Prediction

Abstract: Performative Prediction addresses scenarios where deploying a model induces a distribution shift in the input data, such as individuals modifying their features and reapplying for a bank loan after rejection. Literature has had a theoretical perspective giving mathematical guarantees for convergence (either to the stable or optimal point). We believe that visualization of the loss landscape can complement this theoretical advances with practical insights. Therefore, (1) we introduce a simple decoupled risk visualization method inspired in the two-step process that performative prediction is. Our approach visualizes the risk landscape with respect to two parameter vectors: model parameters and data parameters. We use this method to propose new properties of the interest points, to examine how existing algorithms traverse the risk landscape and perform under more realistic conditions, including strategic classification with non-linear models. (2) Building on this decoupled risk visualization, we introduce a novel setting - extended Performative Prediction - which captures scenarios where the distribution reacts to a model different from the decision-making one, reflecting the reality that agents often lack full access to the deployed model.