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.

翻译：我们提出了一种基于正则化的新算法框架来处理差异最小化问题。通过调整正则化器，我们展示了如何重新诠释算法差异领域中的若干突破性工作，范围涵盖斯宾塞定理 [Spencer 1985, Bansal 2010] 到巴纳斯奇克界 [Banaszczyk 1998, Bansal-Dadush-Garg 2016]。利用我们的技术，我们还证明了在伪随机实例的新场景下，贝克-菲亚拉猜想与科姆洛什猜想成立。