# On the connections between algorithmic regularization and penalization for convex losses

arXiv: https://arxiv.org/abs/1909.03371 · HTML: https://mlsanity.com/paper/1909.03371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Comparing Classes of Estimators: When does Gradient Descent Beat Ridge Regression in Linear Models?](https://mlsanity.com/paper/2108.11872/) (2021)

## Abstract (arXiv)

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.