Implicit Regularization in Matrix Factorization

Suriya Gunasekar, Blake E. Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro

Abstract: We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix X with gradient descent on a factorization of X. We conjecture and provide empirical and theoretical evidence that with small enough step sizes and initialization close enough to the origin, gradient descent on a full dimensional factorization converges to the minimum nuclear norm solution.