# Stochastic optimization with decision-dependent distributions

arXiv: https://arxiv.org/abs/2011.11173 · HTML: https://mlsanity.com/paper/2011.11173/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2020.

## Built on by (most cited first, 30 of 65)

- [Online Decision Transformer](https://mlsanity.com/paper/2202.05607/) (2022)
- [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)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [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)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Stochastic Optimization under Distributional Drift](https://mlsanity.com/paper/2108.07356/) (2021)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [One-Shot Strategic Classification Under Unknown Costs](https://mlsanity.com/paper/2311.02761/) (2023)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Performative Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Approximate Regions of Attraction in Learning with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.00055/) (2021)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Optimal Classification under Performative Distribution Shift](https://mlsanity.com/paper/2411.02023/) (2024)
- [Model Transferability With Responsive Decision Subjects](https://mlsanity.com/paper/2107.05911/) (2021)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Online covariance estimation for stochastic gradient descent under Markovian sampling](https://mlsanity.com/paper/2308.01481/) (2023)
- [Classification Under Strategic Self-Selection](https://mlsanity.com/paper/2402.15274/) (2024)

## Abstract (arXiv)

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features so as to improve the likelihood of being positively labeled. Recent works on performative prediction have identified an intriguing solution concept for such problems: find the decision that is optimal with respect to the static distribution that the decision induces. Continuing this line of work, we show that typical stochastic algorithms -- originally designed for static problems -- can be applied directly for finding such equilibria with little loss in efficiency. The reason is simple to explain: the main consequence of the distributional shift is that it corrupts algorithms with a bias that decays linearly with the distance to the solution. Using this perspective, we obtain sharp convergence guarantees for popular algorithms, such as stochastic gradient, clipped gradient, proximal point, and dual averaging methods, along with their accelerated and proximal variants. In realistic applications, deployment of a decision rule is often much more expensive than sampling. We show how to modify the aforementioned algorithms so as to maintain their sample efficiency while performing only logarithmically many deployments.