# SI-ADMM: A Stochastic Inexact ADMM Framework for Stochastic Convex Programs

arXiv: https://arxiv.org/abs/1711.05286 · HTML: https://mlsanity.com/paper/1711.05286/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [Robust Online Learning over Networks](https://mlsanity.com/paper/2309.00520/) (2023)
- [Distributionally Robust Federated Learning: An ADMM Algorithm](https://mlsanity.com/paper/2503.18436/) (2025)

## Abstract (arXiv)

We consider the structured stochastic convex program requiring the minimization of mathbbE[tilde f(x,xi)]+mathbbE[tilde g(y,xi)] subject to the constraint Ax + By = b. Motivated by the need for decentralized schemes and structure, we propose a stochastic inexact ADMM (SI-ADMM) framework where subproblems are solved inexactly via stochastic approximation schemes. Based on this framework, we prove the following: (i) under suitable assumptions on the associated batch-size of samples utilized at each iteration, the SI-ADMM scheme produces a sequence that converges to the unique solution almost surely; (ii) If the number of gradient steps (or equivalently, the number of sampled gradients) utilized for solving the subproblems in each iteration increases at a geometric rate, the mean-squared error diminishes to zero at a prescribed geometric rate; (iii) The overall iteration complexity in terms of gradient steps (or equivalently samples) is found to be consistent with the canonical level of O(1/ε). Preliminary applications on LASSO and distributed regression suggest that the scheme performs well compared to its competitors.