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arXiv · 1911.05167

Nonconvex Stochastic Nested Optimization via Stochastic ADMM

Zhongruo Wang
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Abstract

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an $\epsilon$ stationary point where the expected norm of the subgradient of corresponding augmented Lagrangian is smaller than $\epsilon$, the total sample complexity of our method is $\mathcal{O}(\epsilon^{-3})$ for the online case and $\mathcal{O} \Bigl((2N_1 + N_2) + (2N_1 + N_2)^{1/2}\epsilon^{-2}\Bigr)$ for the finite sum case. The computational complexity is consistent with proximal version proposed in \cite{zhang2019multi}, but our algorithm can solve more general problem when the proximal mapping of the penalty is not easy to compute.

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Zhongruo Wang. 2019-11-12. Nonconvex Stochastic Nested Optimization via Stochastic ADMM. https://arxiv.org/abs/1911.05167

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