Wasserstein Distributionally Robust Performative Prediction

TL;DR

This paper introduces a Wasserstein distributionally robust framework for performative prediction, accounting for strategic behavior and distribution shifts, with algorithms that converge to stable solutions and bounds on suboptimality.

Contribution

It develops a novel Wasserstein distributionally robust optimization approach for performative prediction, including algorithms with convergence guarantees and theoretical bounds.

Findings

Algorithms converge to a unique stable point.

Explicit bounds on suboptimality gap.

Numerical simulations validate effectiveness.

Abstract

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data samples to adapt to evolving distributions. In this paper, we develop a Wasserstein distributionally robust optimization framework for performative prediction, where the prediction model is optimized over the worst-case distribution within a Wasserstein ambiguity set. We allow the ambiguity radius to depend on the prediction model, which subsumes the constant-radius formulation as a special case. By leveraging strong duality, the intractable robust objective is reformulated as a computationally tractable minimization problem. Based on this formulation, we develop distributionally robust repeated risk minimization (DR-RRM) and repeated gradient descent (DR-RGD), to iteratively find an equilibrium between distributional shifts and model retraining. Theoretical analyses demonstrate that, under standard regularity conditions, both algorithms converge to a unique robust performative stable point. Our analysis explicitly accounts for inner-loop approximation errors and shows convergence to a neighborhood of the stable point in inexact settings. Additionally, we establish theoretical bounds on the suboptimality gap between the stable point and the global performative optimum. Finally, numerical simulations of a dynamic credit scoring problem demonstrate the efficacy of the method.