# On Consensus-Optimality Trade-offs in Collaborative Deep Learning

arXiv: https://arxiv.org/abs/1805.12120 · HTML: https://mlsanity.com/paper/1805.12120/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2018.

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

- [Consensus Control for Decentralized Deep Learning](https://mlsanity.com/paper/2102.04828/) (2021)
- [Cross-Gradient Aggregation for Decentralized Learning from Non-IID data](https://mlsanity.com/paper/2103.02051/) (2021)
- [DIMAT: Decentralized Iterative Merging-And-Training for Deep Learning Models](https://mlsanity.com/paper/2404.08079/) (2024)
- [Provably Convergent Decentralized Optimization over Directed Graphs under Generalized Smoothness](https://mlsanity.com/paper/2601.03566/) (2026)

## Abstract (arXiv)

In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality. In this paper, we build on recent algorithmic progresses in distributed deep learning to explore various consensus-optimality trade-offs over a fixed communication topology. First, we propose the incremental consensus-based distributed SGD (i-CDSGD) algorithm, which involves multiple consensus steps (where each agent communicates information with its neighbors) within each SGD iteration. Second, we propose the generalized consensus-based distributed SGD (g-CDSGD) algorithm that enables us to navigate the full spectrum from complete consensus (all agents agree) to complete disagreement (each agent converges to individual model parameters). We analytically establish convergence of the proposed algorithms for strongly convex and nonconvex objective functions; we also analyze the momentum variants of the algorithms for the strongly convex case. We support our algorithms via numerical experiments, and demonstrate significant improvements over existing methods for collaborative deep learning.