A Proximal Stochastic Gradient Method for Doubly-regularized Spectral Risk Minimization

Spectral risk minimization (SRM) is an important category of distributionally robust optimization. Recent works in this field elaborate on either distribution shift regularization (DSR) on the spectrum or non-differentiable regularization (NDR) on the parameters. However, few methods can simultaneously handle double regularization. The main difficulty lies in suppressing the bias and variance of the stochastic gradient when double regularization is present. To solve this problem, we develop a novel proximal stochastic gradient method (PSG-SRM) that simultaneously handles double regularization, reduces bias and variance along with iterations, and achieves linear convergence. It has lower computational complexity than two state-of-the-art methods that handle DSR or NDR separately. Experimental results indicate that it achieves competitive performance in both regression and classification tasks, and shows stable performance with respect to randomness.