# Distributed saddle-point subgradient algorithms with Laplacian averaging

arXiv: https://arxiv.org/abs/1510.05169 · HTML: https://mlsanity.com/paper/1510.05169/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2015.

## Built on by (most cited first, 5 of 5)

- [Decentralized gradient descent maximization method for composite nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2304.02441/) (2023)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Stochastic Gradient Methods with Compressed Communication for Decentralized Saddle Point Problems](https://mlsanity.com/paper/2205.14452/) (2022)
- [Decentralized Feature-Distributed Optimization for Generalized Linear Models](https://mlsanity.com/paper/2110.15283/) (2021)
- [Switch and Conquer: Efficient Algorithms By Switching Stochastic Gradient Oracles For Decentralized Saddle Point Problems](https://mlsanity.com/paper/2309.00997/) (2023)

## Abstract (arXiv)

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a sum of convex functions in the local variables of the agents. In the latter case, the proposed algorithm reduces to primal-dual updates using local subgradients and Laplacian averaging on local copies of the multipliers associated to the global constraints. For the case of general convex-concave saddle-point problems, our analysis establishes the convergence of the running time-averages of the local estimates to a saddle point under periodic connectivity of the communication digraphs. Specifically, choosing the gradient step-sizes in a suitable way, we show that the evaluation error is proportional to 1/√t, where t is the iteration step. We illustrate our results in simulation for an optimization scenario with nonlinear constraints coupling the decisions of agents that cannot communicate directly.