# Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributions

arXiv: https://arxiv.org/abs/2107.09721 · HTML: https://mlsanity.com/paper/2107.09721/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2021.

## Built on by (most cited first, 17 of 17)

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- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
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- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets](https://mlsanity.com/paper/2404.13240/) (2024)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
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- [The Stability of Online Algorithms in Performative Prediction](https://mlsanity.com/paper/2602.24207/) (2026)
- [Online Decision Making for Trading Wind Energy](https://mlsanity.com/paper/2209.02009/) (2022)
- [Distributionally Time-Varying Online Stochastic Optimization under Polyak-Lojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning](https://mlsanity.com/paper/2309.09411/) (2023)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
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## Abstract (arXiv)

This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online stochastic gradient descent method to solve the optimization, and we provide explicit bounds in expectation and in high probability for the distance between the optimizers and the points generated by the algorithm. In particular, we show that when the gradient error due to sampling is modeled as a sub-Weibull random variable, then the tracking error is ultimately bounded in expectation and in high probability. The theoretical findings are validated via numerical simulations in the context of charging optimization of a fleet of electric vehicles.