Federated Bilevel Performative Prediction

Traditional federated bilevel optimization assumes that client data distributions remain static during training. However, in many real-world applications, the model's decisions influence user behavior and data collection, creating a feedback loop known as performativity. This paper investigates how to perform bilevel optimization in federated systems when both the upper-level (UL) and lower-level (LL) objectives are subject to these decision-dependent distribution shifts.

The authors formalize the Federated Bilevel Performatively Stable (FBPS) point, which characterizes a fixed-point equilibrium where the model's performance is stable despite the distribution shifts induced by its own deployment. To compute this point, they propose two methods:

1. FBi-RRM: A repeated risk minimization approach that converges linearly to the FBPS point under a contraction condition.
2. FBi-SGD: A communication-efficient stochastic method that uses federated hypergradient estimation to handle the nested structure of the problem, providing convergence guarantees with diminishing step sizes.

The framework explicitly accounts for client heterogeneity and the coupled nature of performative shifts across the UL and LL objectives, ensuring that the aggregation process remains effective even when local distributions change.

This work bridges the gap between federated learning and performative prediction. By explicitly modeling the feedback loop between model decisions and data distributions, the proposed methods prevent the instability and bias that occur when performative effects are ignored. The empirical results on strategic regression and meta-classification demonstrate that this awareness leads to better generalization, making it a critical advancement for deploying machine learning models in dynamic, strategic environments.