Stochastic Three-Composite Convex Minimization

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately with their proximal operators, such as doubly regularized empirical risk minimization problems. We prove the convergence characterization of the proposed algorithm in expectation under the standard assumptions for the stochastic gradient estimate of the smooth term. Our method operates in the primal space and can be considered as a stochastic extension of the three-operator splitting method. Numerical evidence supports the effectiveness of our method in real-world problems.


Présenté à:
30th Conference on Neural Information Processing Systems (NIPS2016), Barcelona, Spain, December 5-10, 2016
Année
2016
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 Notice créée le 2016-10-28, modifiée le 2019-03-17

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