# A Decentralized Primal-Dual Framework for Non-convex Smooth Consensus Optimization

arXiv: https://arxiv.org/abs/2107.11321 · HTML: https://mlsanity.com/paper/2107.11321/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2021.

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

- [Variance-reduced accelerated methods for decentralized stochastic double-regularized nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2307.07113/) (2023)
- [Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization](https://mlsanity.com/paper/2508.04950/) (2025)
- [Beyond Centralization: Provable Communication Efficient Decentralized Multi-Task Learning](https://mlsanity.com/paper/2512.22675/) (2025)
- [LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication](https://mlsanity.com/paper/2604.09970/) (2026)
- [Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization](https://mlsanity.com/paper/2606.28307/) (2026)

## Abstract (arXiv)

In this work, we introduce ADAPD, A DecentrAlized Primal-Dual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. The proposed framework relies on a novel problem formulation that elicits ADMM-type updates, where each agent first inexactly solves a local strongly convex subproblem with any method of its choice and then performs a neighbor communication to update a set of dual variables. We present two variants that allow for a single gradient step for the primal updates or multiple communications for the dual updates, to exploit the tradeoff between the per-iteration cost and the number of iterations. When multiple communications are performed, ADAPD can achieve theoretically optimal communication complexity results for non-convex and smooth consensus problems. Numerical experiments on several applications, including a deep-learning one, demonstrate the superiority of ADAPD over several popularly used decentralized methods.