Distributionally Robust Performative Optimization

TL;DR

This paper introduces a distributionally robust framework for performative stochastic optimization that accounts for distribution ambiguity, proposing an iterative algorithm with theoretical guarantees and demonstrating superior performance in various applications.

Contribution

It develops a novel distributionally robust approach for performative optimization, addressing distribution ambiguity and proposing an efficient iterative solution method.

Findings

The proposed method improves robustness to distribution misspecification.

The algorithm converges with theoretical guarantees.

Numerical experiments show significant performance gains.

Abstract

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true distribution map and must instead rely on imperfect surrogate models, which can lead to severely suboptimal solutions under misspecification. Data scarcity or costly collection further exacerbates these challenges in real-world settings. To address these challenges, we propose a distributionally robust framework for performative optimization that explicitly accounts for ambiguity in the decision-dependent distribution. Our framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty. This latter setting has not previously been explored in the performative optimization literature. To tackle the intractability of the resulting nonconvex objectives, we develop an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision. This decoupling ensures computational tractability at each iteration while enhancing robustness to model uncertainty. We provide reformulations compatible with off-the-shelf solvers and establish theoretical guarantees on convergence and suboptimality. Extensive numerical experiments in strategic classification, revenue management, and portfolio optimization demonstrate significant performance gains over state-of-the-art baselines, highlighting the practical value of our approach.