# Honest Inference for Stochastic Optimization

arXiv: https://arxiv.org/abs/2501.07772 · HTML: https://mlsanity.com/paper/2501.07772/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2025.

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

- [On the Precise Asymptotics of Universal Inference](https://mlsanity.com/paper/2503.14717/) (2025)
- [Optimal Inference with Black-box Predictions](https://mlsanity.com/paper/2608.10155/) (2026)

## Abstract (arXiv)

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. We provide a unified treatment of validity, conservativeness, and the size of the resulting confidence sets. In particular, the presented width analysis demonstrates the adaptive behavior of the confidence set to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems. Numerical results for all statistical applications are provided.