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

arXiv: https://arxiv.org/abs/2607.26562 · HTML: https://mlsanity.com/paper/2607.26562/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Loss Functions and Metrics in Deep Learning](https://mlsanity.com/paper/2307.02694/) (2023)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization](https://mlsanity.com/paper/2212.05088/) (2022)
- [Zeroth-Order Methods for Nonconvex Stochastic Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2412.20330/) (2024)
- [Zeroth-order gradient estimators for stochastic problems with decision-dependent distributions](https://mlsanity.com/paper/2510.24929/) (2025)

## Abstract (arXiv)

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.