A Unified Inexact Stochastic ADMM for Composite Nonconvex and Nonsmooth Optimization
arxiv(2024)
摘要
In this paper, we propose a unified framework of inexact stochastic
Alternating Direction Method of Multipliers (ADMM) for solving nonconvex
problems subject to linear constraints, whose objective comprises an average of
finite-sum smooth functions and a nonsmooth but possibly nonconvex function.
The new framework is highly versatile. Firstly, it not only covers several
existing algorithms such as SADMM, SVRG-ADMM, and SPIDER-ADMM but also guides
us to design a novel accelerated hybrid stochastic ADMM algorithm, which
utilizes a new hybrid estimator to trade-off variance and bias. Second, it
enables us to exploit a more flexible dual stepsize in the convergence
analysis. Under some mild conditions, our unified framework preserves
𝒪(1/T) sublinear convergence. Additionally, we establish the linear
convergence under error bound conditions. Finally, numerical experiments
demonstrate the efficacy of the new algorithm for some nonsmooth and nonconvex
problems.
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