# Online Saddle Point Tracking with Decision-Dependent Data

arXiv: https://arxiv.org/abs/2212.02693 · HTML: https://mlsanity.com/paper/2212.02693/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2022.

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional dependence via a distributional map, and are known to have two distinct types of solutions--saddle points and equilibrium points. We demonstrate that, under suitable conditions, online primal-dual type algorithms are capable of tracking equilibrium points. In contrast, since computing closed-form gradient of the objective requires knowledge of the distributional map, we offer an online stochastic primal-dual algorithm for tracking equilibrium trajectories. We provide bounds in expectation and in high probability, with the latter leveraging a sub-Weibull model for the gradient error. We illustrate our results on an electric vehicle charging problem where responsiveness to prices follows a location-scale family based distributional map.