Performative Multi-Objective Optimization

Performative prediction studies learning under model-induced distribution shift, where the deployed model shapes the very data it aims to predict. Existing theory and algorithms largely focus on a single objective or collapse multiple criteria into one aggregated loss, while practical systems may involve several potentially conflicting objectives such as accuracy, fairness, robustness, and welfare. We introduce performative multi-objective optimization (PMOO), a framework for jointly optimizing several performative objectives, and define Performative Pareto Stationary (PPS) points as solutions satisfying the first-order Pareto stationarity condition under the environment induced by the deployed model. A central challenge in PMOO is the coupling between $\text{environmental drift}$, induced by the deployed model, and $\text{multiplier drift}$, reflecting evolving trade-offs among objectives. Deployment affects the gradient geometry used to select the multiplier weights, while these weights shape model updates and subsequent environments. For smooth nonconvex objectives, we analyze multi-gradient descent (MGD) and show that its best iterate attains approximate PPS. To stabilize the multiplier dynamics, we propose proximal MGD (PMGD). In the strongly convex setting, we further develop a coupled convergence analysis that makes explicit how performative sensitivity and multiplier geometry influence the dynamics. Together, these results extend performative prediction to a Pareto framework for learning with conflicting objectives.