DeepAI AI Chat
Log In Sign Up

Nonconvex Stochastic Nested Optimization via Stochastic ADMM

by   Zhongruo Wang, et al.

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 ϵ stationary point where the expected norm of the subgradient of corresponding augmented Lagrangian is smaller than ϵ, the total sample complexity of our method is O(ϵ^-3) for the online case and O((2N_1 + N_2) + (2N_1 + N_2)^1/2ϵ^-2) for the finite sum case. The computational complexity is consistent with proximal version proposed in <cit.>, but our algorithm can solve more general problem when the proximal mapping of the penalty is not easy to compute.


page 1

page 2

page 3

page 4


Multi-Level Composite Stochastic Optimization via Nested Variance Reduction

We consider multi-level composite optimization problems where each mappi...

Accelerating Stochastic Composition Optimization

Consider the stochastic composition optimization problem where the objec...

Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates

In this paper, we study smooth stochastic multi-level composition optimi...

Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization

We consider the stochastic composition optimization problem proposed in ...

Adaptive Stochastic Alternating Direction Method of Multipliers

The Alternating Direction Method of Multipliers (ADMM) has been studied ...

Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization

Many real-world problems not only have complicated nonconvex functional ...