The paper provides stochastic algorithms with O(1/epsilon^{4/v}) iteration complexity for finding near-stationary points of non-convex inf-projection objectives, with a variance-regularization application.
SPRING: A fast stochastic proximal alternating method for non-smooth non-convex optimization
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abstract
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to advances in data acquisition and computational capabilities. Motivated by the success of stochastic optimization methods, we propose a stochastic variant of proximal alternating linearized minimization (PALM) algorithm \cite{bolte2014proximal}. We provide global convergence guarantees, demonstrating that our proposed method with variance-reduced stochastic gradient estimators, such as SAGA \cite{SAGA} and SARAH \cite{sarah}, achieves state-of-the-art oracle complexities. We also demonstrate the efficacy of our algorithm via several numerical examples including sparse non-negative matrix factorization, sparse principal component analysis, and blind image deconvolution.
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2019 1verdicts
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Stochastic Optimization for Non-convex Inf-Projection Problems
The paper provides stochastic algorithms with O(1/epsilon^{4/v}) iteration complexity for finding near-stationary points of non-convex inf-projection objectives, with a variance-regularization application.