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The Cartographer
Discrepancy Minimization via Regularization
November 10, 2022 Β· Declared Dead Β· π ACM-SIAM Symposium on Discrete Algorithms
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Authors
Lucas Pesenti, Adrian Vladu
arXiv ID
2211.05509
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.DM
Citations
12
Venue
ACM-SIAM Symposium on Discrete Algorithms
Last Checked
3 months ago
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 KomlΓ³s conjectures are true in a new regime of pseudorandom instances.
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