mlsanityData to 7 Oct 2026

Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality

arXiv 2207.04173 ↗First posted 9 Jul 2022math.OC cs.LG stat.MLcited by 12

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Abstract (arXiv)

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction and its multiplayer extensions. We show that under mild assumptions, the deviation between the average iterate of the algorithm and the solution is asymptotically normal, with a covariance that clearly decouples the effects of the gradient noise and the distributional shift. Moreover, building on the work of H'ajek and Le Cam, we show that the asymptotic performance of the algorithm with averaging is locally minimax optimal.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 18 of its 46 references that are in the map. First posted on arXiv 9 Jul 2022.

Builds on

18 of 46 references.

References · 18

  1. 2020Performative Predictioncited by 318
  2. 2015Strategic Classificationcited by 256
  3. 2017Strategic Classification from Revealed Preferencescited by 126
  4. 2021Outside the Echo Chamber: Optimizing the Performative Riskcited by 95
  5. 2019Strategic Classification is Causal Modeling in Disguisecited by 92
  6. 2020Stochastic Optimization for Performative Predictioncited by 92
  7. 2020Performative Prediction in a Stateful Worldcited by 90
  8. 2021How to Learn when Data Reacts to Your Model: Performative Gradient Descentcited by 70
  9. 2020Stochastic optimization with decision-dependent distributionscited by 65
  10. 2022Multiplayer Performative Prediction: Learning in Decision-Dependent Gamescited by 42
  11. 2022Regret Minimization with Performative Feedbackcited by 40
  12. 2016Asymptotic Optimality in Stochastic Optimizationcited by 38
6 more
  1. 2022Multi-agent Performative Prediction: From Global Stability and Optimality to Chaoscited by 33
  2. 2022Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environmentscited by 31
  3. 2021Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributionscited by 17
  4. 2020Gaming Helps! Learning from Strategic Interactions in Natural Dynamicscited by 14
  5. 2021Stochastic Optimization under Distributional Driftcited by 13
  6. 2022Stochastic Saddle Point Problems with Decision-Dependent Distributionscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 4; 2026: 5.

12 papers.

  1. 2023Performative Prediction: Past and Futurecited by 52
  2. 2023Asymptotic normality and optimality in nonsmooth stochastic approximationcited by 14
  3. 2025Statistical Inference under Performativitycited by 4
  4. 2025Statistical Inference for Online Algorithmscited by 2
  5. 2025Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutionscited by 1
  6. 2026Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Frameworkcited by 1
  7. 2024The radius of statistical efficiencycited by 0
  8. 2025Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Mapscited by 0
  9. 2026When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learningcited by 0
  10. 2026Performative Learning Theorycited by 0
  11. 2026Adaptive Conditional Forest Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertaintycited by 0
  12. 2026When and How Human Curation Backfires: Preference Alignment under Multi-Model Self-Consuming Loopcited by 0