Distributionally Robust Performative Prediction

TL;DR

This paper introduces a distributionally robust framework for performative prediction that provides guarantees and improved robustness against distribution map misspecification, enhancing performance in dynamic systems.

Contribution

It proposes the distributionally robust performative optimum (DRPO), a new solution concept with provable guarantees and an efficient reformulation for robust performative prediction.

Findings

DRPO offers robustness against distribution map misspecification.

The reformulation enables efficient optimization of the robust solution.

Experimental results show advantages over traditional performative optimum.

Abstract

Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target. The pursuit of a performative optimum (PO) -- minimizing performative risk -- is generally reliant on modeling of the distribution map, which characterizes how a deployed ML model alters the data distribution. Unfortunately, inevitable misspecification of the distribution map can lead to a poor approximation of the true PO. To address this issue, we introduce a novel framework of distributionally robust performative prediction and study a new solution concept termed as distributionally robust performative optimum (DRPO). We show provable guarantees for DRPO as a robust approximation to the true PO when the nominal distribution map is different from the actual one. Moreover, distributionally robust performative prediction can be reformulated as an augmented performative prediction problem, enabling efficient optimization. The experimental results demonstrate that DRPO offers potential advantages over traditional PO approach when the distribution map is misspecified at either micro- or macro-level.