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

What the math gives to ML

The paper provides a constructive way to optimize objectives whose data distribution changes as a function of deployed parameters, rather than treating the data distribution as fixed. Its transferable asset is a sphere-smoothed, finite-difference estimator of the Jacobian of the induced distribution shift, together with an explicit bias-variance bound that exposes the roles of perturbation radius, direction batch size, observation batch size, and noise. A neural-network optimizer can use this Jacobian to add the missing distribution-response term to the ordinary training gradient, yielding a feedback-aware update for models deployed in environments where predictions alter future samples. The most direct test is a classifier or recommender connected to a differentiable or simulated user/environment response model, comparing standard SGD against the Jacobian-corrected update at equal environment-rollout cost.