Discrepancy Minimization via Regularization

11/10/2022

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by   Lucas Pesenti, et al.

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Università Bocconi

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IRIF

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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 Komlós conjectures are true in a new regime of pseudorandom instances.