# Random tilts to find stationary points in stochastic convex optimization

arXiv: https://arxiv.org/abs/2609.17798 · HTML: https://mlsanity.com/paper/2609.17798/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Improving the Privacy and Practicality of Objective Perturbation for Differentially Private Linear Learners](https://mlsanity.com/paper/2401.00583/) (2023)
- [Unbiased estimators for random design regression](https://mlsanity.com/paper/1907.03411/) (2019)
- [Failure of uniform laws of large numbers for subdifferentials and beyond](https://mlsanity.com/paper/2511.16568/) (2025)
- [Finding a stationary point of a stochastic convex problem](https://mlsanity.com/paper/2607.06883/) (2026)

## Abstract (arXiv)

We consider the problem of finding stationary points of stochastic convex functions and related variational inequalities. For each, we show that regularized empirical risk minimization, coupled with a random tilting perturbation, obtains stationarity residual order √d/n for d-dimensional problems given n observations. We present a few complementary results that show that some dimension dependence is necessary, in distinction from standard stochastic optimization and empirical risk minimization, by providing minimax lower bounds scaling as √log d / n.