Distributionally Robust Performative Optimization

In this paper, we propose a general distributionally robust framework for performative optimization, where the selected decision can influence the probabilistic distribution of uncertain parameters. Our framework facilitates safe decision-making in scenarios with incomplete information about the underlying decision-dependent distributions, relying instead on accessible reference distributions. To tackle the challenge of decision-dependent uncertainty, we introduce an algorithm named repeated robust risk minimization. This algorithm decouples the decision variables associated with the ambiguity set from the expected loss, optimizing the latter at each iteration while keeping the former fixed to the previous decision. By leveraging the strong connection between distributionally robust optimization and regularization, we establish a linear convergence rate to a performatively stable point and provide a suboptimality performance guarantee for the proposed algorithm. Finally, we examine the performance of our proposed model through an experimental study in strategic classification.