Discrepancy Minimization via Regularization

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 [Spe85, Ban10] to Banaszczyk's bounds [Ban98, BDG19]. Using our techniques, we also show that the Beck-Fiala and Komlós conjectures are true in a new regime of pseudorandom instances.