# Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments

arXiv: https://arxiv.org/abs/2204.08281 · HTML: https://mlsanity.com/paper/2204.08281/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 8 Apr 2022.

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

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm](https://mlsanity.com/paper/1902.03736/) (2019)
- [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)
- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Bandit learning in concave N-person games](https://mlsanity.com/paper/1810.01925/) (2018)
- [Algorithms for Hiring and Outsourcing in the Online Labor Market](https://mlsanity.com/paper/2002.07618/) (2020)
- [Optimizing Curbside Parking Resources Subject to Congestion Constraints](https://mlsanity.com/paper/1703.07802/) (2017)

## Built on by (most cited first, 30 of 32)

- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Distributionally Robust Performative Prediction](https://mlsanity.com/paper/2412.04346/) (2024)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Emergent specialization from participation dynamics and multi-learner retraining](https://mlsanity.com/paper/2206.02667/) (2022)
- [Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flows](https://mlsanity.com/paper/2307.01166/) (2023)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [The Stability of Online Algorithms in Performative Prediction](https://mlsanity.com/paper/2602.24207/) (2026)
- [On the Impact of Performative Risk Minimization for Binary Random Variables](https://mlsanity.com/paper/2502.02331/) (2025)
- [Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions](https://mlsanity.com/paper/2402.15188/) (2024)
- [Risk-averse Learning with Non-Stationary Distributions](https://mlsanity.com/paper/2404.02988/) (2024)
- [SPRINT: Stochastic Performative Prediction With Variance Reduction](https://mlsanity.com/paper/2509.17304/) (2025)
- [Achieve Performatively Optimal Policy for Performative Reinforcement Learning](https://mlsanity.com/paper/2510.04430/) (2025)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [Partially Performative Prediction](https://mlsanity.com/paper/2606.07890/) (2026)
- [Retraining Seeks Stable Signals](https://mlsanity.com/paper/2607.15623/) (2026)
- [Risk-averse learning with delayed feedback](https://mlsanity.com/paper/2409.16866/) (2024)
- [Evolutionary Prediction Games](https://mlsanity.com/paper/2503.03401/) (2025)
- [Risk-Averse Learning with Varying Risk Levels](https://mlsanity.com/paper/2512.22986/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)

## Abstract (arXiv)

This paper studies the problem of expected loss minimization given a data distribution that is dependent on the decision-maker's action and evolves dynamically in time according to a geometric decay process. Novel algorithms for both the information setting in which the decision-maker has a first order gradient oracle and the setting in which they have simply a loss function oracle are introduced. The algorithms operate on the same underlying principle: the decision-maker repeatedly deploys a fixed decision over the length of an epoch, thereby allowing the dynamically changing environment to sufficiently mix before updating the decision. The iteration complexity in each of the settings is shown to match existing rates for first and zero order stochastic gradient methods up to logarithmic factors. The algorithms are evaluated on a "semi-synthetic" example using real world data from the SFpark dynamic pricing pilot study; it is shown that the announced prices result in an improvement for the institution's objective (target occupancy), while achieving an overall reduction in parking rates.