Distribution Free M-estimation

Felipe Areces, John Duchi
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3619-3627, 2026.

Abstract

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-areces26a, title = { Distribution Free M-estimation }, author = {Areces, Felipe and Duchi, John}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3619--3627}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/areces26a/areces26a.pdf}, url = {https://proceedings.mlr.press/v300/areces26a.html}, abstract = { 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 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. } }
Endnote
%0 Conference Paper %T Distribution Free M-estimation %A Felipe Areces %A John Duchi %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-areces26a %I PMLR %P 3619--3627 %U https://proceedings.mlr.press/v300/areces26a.html %V 300 %X 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 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.
APA
Areces, F. & Duchi, J.. (2026). Distribution Free M-estimation . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3619-3627 Available from https://proceedings.mlr.press/v300/areces26a.html.

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