# Distribution free M-estimation

arXiv: https://arxiv.org/abs/2505.22807 · HTML: https://mlsanity.com/paper/2505.22807/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Lower Bounds for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1912.02365/) (2019)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [How To Make the Gradients Small Stochastically: Even Faster Convex and Nonconvex SGD](https://mlsanity.com/paper/1801.02982/) (2018)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Gradient Equilibrium in Online Learning: Theory and Applications](https://mlsanity.com/paper/2501.08330/) (2025)
- [Local Minimax Complexity of Stochastic Convex Optimization](https://mlsanity.com/paper/1605.07596/) (2016)
- [How to trap a gradient flow](https://mlsanity.com/paper/2001.02968/) (2020)

## Built on by (most cited first, 1 of 1)

- [Finding a stationary point of a stochastic convex problem](https://mlsanity.com/paper/2607.06883/) (2026)

## Abstract (arXiv)

The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex M-estimation or stochastic optimization problem is solvable in such an assumption-free setting, providing a precise dividing line between solvable and unsolvable problems. The conditions we identify show, perhaps surprisingly, that Lipschitz continuity of the loss being minimized is not necessary for distribution free minimization, and they are also distinct from classical characterizations of learnability in machine learning.