On the connections between algorithmic regularization and penalization for convex losses

09/08/2019

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by   Qian Qian, et al.

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In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a condition is satisfied, the optimization path of an iterative algorithm on the unregularized optimization problem can be represented as the solution path of a corresponding penalized problem.