# Stochastic Optimization Schemes for Performative Prediction with Nonconvex Loss

arXiv: https://arxiv.org/abs/2405.17922 · HTML: https://mlsanity.com/paper/2405.17922/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2024.

## Built on by (most cited first, 13 of 13)

- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [SPRINT: Stochastic Performative Prediction With Variance Reduction](https://mlsanity.com/paper/2509.17304/) (2025)
- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [When and How Human Curation Backfires: Preference Alignment under Multi-Model Self-Consuming Loop](https://mlsanity.com/paper/2605.29267/) (2026)
- [Think, Act, Learn: A Framework for Autonomous Robotic Agents using Closed-Loop Large Language Models](https://mlsanity.com/paper/2507.19854/) (2025)
- [Strategically Deceptive Model Deployment in Performative Prediction](https://mlsanity.com/paper/2506.09044/) (2025)
- [Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps](https://mlsanity.com/paper/2509.02619/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)
- [Performative Learning Theory](https://mlsanity.com/paper/2602.04402/) (2026)
- [Local and Global Stability in Performative Reinforcement Learning](https://mlsanity.com/paper/2609.06467/) (2026)
- [Partially Informed Stochastic Optimization via Zeroth-Order Residual Tracking](https://mlsanity.com/paper/2610.13871/) (2026)

## Abstract (arXiv)

This paper studies a risk minimization problem with decision dependent data distribution. The problem pertains to the performative prediction setting in which a trained model can affect the outcome estimated by the model. Such dependency creates a feedback loop that influences the stability of optimization algorithms such as stochastic gradient descent (SGD). We present the first study on performative prediction with smooth but possibly non-convex loss. We analyze a greedy deployment scheme with SGD (SGD-GD). Note that in the literature, SGD-GD is often studied with strongly convex loss. We first propose the definition of stationary performative stable (SPS) solutions through relaxing the popular performative stable condition. We then prove that SGD-GD converges to a biased SPS solution in expectation. We consider two conditions of sensitivity on the distribution shifts: (i) the sensitivity is characterized by Wasserstein-1 distance and the loss is Lipschitz w.r.t.~data samples, or (ii) the sensitivity is characterized by total variation (TV) divergence and the loss is bounded. In both conditions, the bias levels are proportional to the stochastic gradient's variance and sensitivity level. Our analysis is extended to a lazy deployment scheme where models are deployed once per several SGD updates, and we show that it converges to an SPS solution with reduced bias. Numerical experiments corroborate our theories.