Discrepancy Minimization via Regularization
Data Structures and Algorithms
2026-04-15 v2 Discrete Mathematics
Abstract
We introduce a new algorithmic framework for discrepancy minimization based on regularization. We demonstrate how varying the regularizer allows us to re-interpret several breakthrough works in algorithmic discrepancy, ranging from Spencer's theorem [Spencer 1985, Bansal 2010] to Banaszczyk's bounds [Banaszczyk 1998, Bansal-Dadush-Garg 2016]. Using our techniques, we also show that the Beck-Fiala and Komlos conjectures are true in a new regime of pseudorandom instances.
Keywords
Cite
@article{arxiv.2211.05509,
title = {Discrepancy Minimization via Regularization},
author = {Lucas Pesenti and Adrian Vladu},
journal= {arXiv preprint arXiv:2211.05509},
year = {2026}
}
Comments
Updated to include an erratum: the constant in Theorem 4.5 is corrected from 3.7 to 4.1. We thank Haotian Jiang and Nikhil Bansal for identifying the error