# Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics arXiv: https://arxiv.org/abs/2503.07324 ยท HTML: https://mlsanity.com/paper/2503.07324/ ## Key facts - Cited by 6 papers in the map (data through 14 Oct 2026). - Builds on 44 of its 59 references that are in the map. - First posted on arXiv 10 Mar 2025. ## Builds on (most cited first, 30 of 44) - [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016) - [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013) - [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018) - [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020) - [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018) - [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) - [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021) - [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) - [A High Probability Analysis of Adaptive SGD with Momentum](https://mlsanity.com/paper/2007.14294/) (2020) - [Learning in Mean Field Games: A Survey](https://mlsanity.com/paper/2205.12944/) (2022) - [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023) - [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021) - [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022) - [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) - [High Probability Convergence Bounds for Non-convex Stochastic Gradient Descent with Sub-Weibull Noise](https://mlsanity.com/paper/2006.05610/) (2020) - [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020) - [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (2022) - [Online Stochastic Optimization with Wasserstein Based Non-stationarity](https://mlsanity.com/paper/2012.06961/) (2020) - [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (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) - [Polarization in Geometric Opinion Dynamics](https://mlsanity.com/paper/2106.12459/) (2021) - [A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part I](https://mlsanity.com/paper/1701.06307/) (2017) - [Stochastic Optimization under Distributional Drift](https://mlsanity.com/paper/2108.07356/) (2021) ## Built on by (most cited first, 6 of 6) - [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025) - [Efficient Model-Based Reinforcement Learning for Robot Control via Online Optimization](https://mlsanity.com/paper/2510.18518/) (2025) - [A Systems-Theoretic View on the Convergence of Algorithms under Disturbances](https://mlsanity.com/paper/2512.17598/) (2025) - [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026) - [Robust Strategic Classification under Decision-Dependent Cost Uncertainty](https://mlsanity.com/paper/2606.30136/) (2026) - [Foundations of Reinforcement Learning and Control:Connections and New Perspectives](https://mlsanity.com/paper/2608.02433/) (2026) ## Abstract (arXiv) Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects the environment and alters the data-generating distribution. In the realm of performative prediction, this is encoded by distribution maps parameterized by decisions due to strategic behaviors. In contrast, we formalize an endogenous distribution shift as a feedback process featuring nonlinear dynamics that couple the evolving distribution with the decision. Stochastic optimization in this dynamic regime provides a fertile ground to examine the various roles played by dynamics in the composite problem structure. To this end, we develop an online algorithm that achieves optimal decision-making by both adapting to and shaping the dynamic distribution. Throughout the paper, we adopt a distributional perspective and demonstrate how this view facilitates characterizations of distribution dynamics and the optimality and generalization performance of the proposed algorithm. We showcase the theoretical results in an opinion dynamics context, where an opportunistic party maximizes the affinity of a dynamic polarized population, and in a recommender system scenario, featuring performance optimization with discrete distributions in the probability simplex.