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This paper introduces a novel gradient-based optimization method tailored for performative prediction, where model deployment influences future data distributions. By relaxing the assumptions on data distributions and loss functions, the proposed method utilizes finite differences to estimate distribution shifts, enabling effective optimization in higher dimensions. Experimental results reveal that this approach not only converges faster but also maintains consistency across a wider range of scenarios compared to existing methods.
Existing optimization methods falter under performative prediction, but our new approach guarantees convergence with fewer assumptions and faster results.
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.