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

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.