# Communication-Censored Linearized ADMM for Decentralized Consensus Optimization

arXiv: https://arxiv.org/abs/1909.06724 · HTML: https://mlsanity.com/paper/1909.06724/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Decentralized Federated Learning: Balancing Communication and Computing Costs](https://mlsanity.com/paper/2107.12048/) (2021)
- [Provable Privacy Advantages of Decentralized Federated Learning via Distributed Optimization](https://mlsanity.com/paper/2407.09324/) (2024)
- [FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data](https://mlsanity.com/paper/2504.11903/) (2025)
- [Adaptive Decentralized Federated Learning for Robust Optimization](https://mlsanity.com/paper/2512.02852/) (2025)

## Abstract (arXiv)

In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node updates its local variable through combining neighboring variables and solving an optimization subproblem. The proposed algorithm, called as COmmunication-censored Linearized ADMM (COLA), leverages a linearization technique to reduce the iteration-wise computation cost of ADMM and uses a communication-censoring strategy to alleviate the communication cost. To be specific, COLA introduces successive linearization approximations to the local cost functions such that the resultant computation is first-order and light-weight. Since the linearization technique slows down the convergence speed, COLA further adopts the communication-censoring strategy to avoid transmissions of less informative messages. A node is allowed to transmit only if the distance between the current local variable and its previously transmitted one is larger than a censoring threshold. COLA is proven to be convergent when the local cost functions have Lipschitz continuous gradients and the censoring threshold is summable. When the local cost functions are further strongly convex, we establish the linear (sublinear) convergence rate of COLA, given that the censoring threshold linearly (sublinearly) decays to 0. Numerical experiments corroborate with the theoretical findings and demonstrate the satisfactory communication-computation tradeoff of COLA.