# A Fully Stochastic Primal-Dual Algorithm

arXiv: https://arxiv.org/abs/1901.08170 · HTML: https://mlsanity.com/paper/1901.08170/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [A Stochastic Approximation Approach for Efficient Decentralized Optimization on Random Networks](https://mlsanity.com/paper/2410.18774/) (2024)

## Abstract (arXiv)

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations are unknown but revealed across time through i.i.d. realizations. The proposed algorithm is proven to converge to a saddle point of the Lagrangian function. In the framework of the monotone operator theory, the convergence proof relies on recent results on the stochastic Forward Backward algorithm involving random monotone operators. An example of convex optimization under stochastic linear constraints is considered.