# Zero-Regret Performative Prediction Under Inequality Constraints

arXiv: https://arxiv.org/abs/2309.12618 · HTML: https://mlsanity.com/paper/2309.12618/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 38 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Non-asymptotic Analysis of Biased Stochastic Approximation Scheme](https://mlsanity.com/paper/1902.00629/) (2019)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (2022)
- [Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents](https://mlsanity.com/paper/2209.03811/) (2022)
- [Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.09721/) (2021)
- [Teaching the Old Dog New Tricks: Supervised Learning with Constraints](https://mlsanity.com/paper/2002.10766/) (2020)
- [Stochastic Primal-Dual Algorithms with Faster Convergence than O(1/√T) for Problems without Bilinear Structure](https://mlsanity.com/paper/1904.10112/) (2019)
- [Stochastic Primal-Dual Method for Empirical Risk Minimization with O(1) Per-Iteration Complexity](https://mlsanity.com/paper/1811.01182/) (2018)
- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Knowledge Enhanced Hybrid Neural Network for Text Matching](https://mlsanity.com/paper/1611.04684/) (2016)
- [Online Saddle Point Tracking with Decision-Dependent Data](https://mlsanity.com/paper/2212.02693/) (2022)

## Built on by (most cited first, 10 of 10)

- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [On Corruption-Robustness in Performative Reinforcement Learning](https://mlsanity.com/paper/2505.05609/) (2025)
- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Decentralized Multi-Task Online Convex Optimization Under Random Link Failures](https://mlsanity.com/paper/2401.02011/) (2024)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)
- [Partially Performative Prediction](https://mlsanity.com/paper/2606.07890/) (2026)
- [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)

## Abstract (arXiv)

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many real-world learning problems are subject to constraints. This paper bridges this gap by studying performative prediction under inequality constraints. Unlike most existing work that provides only performative stable points, we aim to find the optimal solutions. Anticipating performative gradients is a challenging task, due to the agnostic performative effect on data distributions. To address this issue, we first develop a robust primal-dual framework that requires only approximate gradients up to a certain accuracy, yet delivers the same order of performance as the stochastic primal-dual algorithm without performativity. Based on this framework, we then propose an adaptive primal-dual algorithm for location families. Our analysis demonstrates that the proposed adaptive primal-dual algorithm attains caO(√T) regret and constraint violations, using only √T + 2T samples, where T is the time horizon. To our best knowledge, this is the first study and analysis on the optimality of the performative prediction problem under inequality constraints. Finally, we validate the effectiveness of our algorithm and theoretical results through numerical simulations.