Adaptive Gradient-Based Methods for a Broader Class of Optimization Problems under Performative Prediction

2026-07-29

AI Summary

This work addresses the challenge in performative prediction where model deployment induces distributional shifts that complicate optimization. Existing approaches often rely on strong assumptions about the loss function and data distribution, limiting their applicability. To overcome this, the paper proposes a gradient-based adaptive optimization algorithm that explicitly estimates deployment-induced distribution shifts via finite differences, thereby accommodating a broader class of losses and distributions without stringent assumptions. The method supports high-dimensional optimization and incorporates a sample-efficient approximation strategy to reduce data requirements. Theoretical analysis establishes convergence guarantees for the proposed algorithm. Empirical results demonstrate that it converges faster and more stably than existing methods, exhibiting superior robustness and practicality across diverse experimental settings.

Abstract

We study optimization under performative prediction, where deploying a model affects the future data distribution. For this setting, several gradient-based approaches have been proposed. However, they typically assume specific data distributions or loss functions, which limit their practical applicability. To overcome these limitations, we propose a gradient-based optimization method with convergence guarantees under substantially weaker assumptions. Our method explicitly estimates the induced distribution shift through finite differences. It enables higher-dimensional optimization across broader classes of loss functions and data distributions. We also propose a practical variant that reduces the number of samples required. Numerical experiments demonstrate that our proposed algorithms converge faster and more consistently than existing ones.

Problem

• performative prediction
• optimization
• gradient-based methods
• distribution shift
• loss functions

Innovation

• performative prediction
• adaptive gradient method
• distribution shift estimation
• finite differences
• convergence under weak assumptions