# Mini-Batch Stochastic ADMMs for Nonconvex Nonsmooth Optimization

arXiv: https://arxiv.org/abs/1802.03284 · HTML: https://mlsanity.com/paper/1802.03284/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Stochastic Block-ADMM for Training Deep Networks](https://mlsanity.com/paper/2105.00339/) (2021)
- [Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum](https://mlsanity.com/paper/2504.12742/) (2025)
- [DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing](https://mlsanity.com/paper/2510.18218/) (2025)

## Abstract (arXiv)

With the large rising of complex data, the nonconvex models such as nonconvex loss function and nonconvex regularizer are widely used in machine learning and pattern recognition. In this paper, we propose a class of mini-batch stochastic ADMMs (alternating direction method of multipliers) for solving large-scale nonconvex nonsmooth problems. We prove that, given an appropriate mini-batch size, the mini-batch stochastic ADMM without variance reduction (VR) technique is convergent and reaches a convergence rate of O(1/T) to obtain a stationary point of the nonconvex optimization, where T denotes the number of iterations. Moreover, we extend the mini-batch stochastic gradient method to both the nonconvex SVRG-ADMM and SAGA-ADMM proposed in our initial manuscript citehuang2016stochastic, and prove these mini-batch stochastic ADMMs also reaches the convergence rate of O(1/T) without condition on the mini-batch size. In particular, we provide a specific parameter selection for step size η of stochastic gradients and penalty parameter ρ of augmented Lagrangian function. Finally, extensive experimental results on both simulated and real-world data demonstrate the effectiveness of the proposed algorithms.