Adaptive Gradient-Based Methods for a Broader Class of Optimization Problems under Performative Prediction
arXiv:2607.26562
The paper proposes a gradient-based optimization algorithm that estimates distribution shifts via finite differences, providing convergence guarantees for a wider range of loss functions and data distributions in performative prediction 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.
31pages, 2 figures