Simple Stochastic Gradient Methods for Non-Smooth Non-Convex Regularized Optimization


Michael Metel, Akiko Takeda ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4537-4545, 2019.


Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence results have been reported. We present two simple stochastic gradient algorithms, for finite-sum and general stochastic optimization problems, which have superior convergence complexities compared to the current state-of-the-art. We also compare our algorithms’ performance in practice for empirical risk minimization.

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