# Zeroth Order Nonconvex Multi-Agent Optimization over Networks

arXiv: https://arxiv.org/abs/1710.09997 · HTML: https://mlsanity.com/paper/1710.09997/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2017.

## Built on by (most cited first, 13 of 13)

- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [On the Convergence of Zeroth-Order Federated Tuning for Large Language Models](https://mlsanity.com/paper/2402.05926/) (2024)
- [Distributed Multi-Agent Reinforcement Learning Based on Graph-Induced Local Value Functions](https://mlsanity.com/paper/2202.13046/) (2022)
- [Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent](https://mlsanity.com/paper/2107.12416/) (2021)
- [Decentralized Multi-Task Stochastic Optimization With Compressed Communications](https://mlsanity.com/paper/2112.12373/) (2021)
- [Lazy Queries Can Reduce Variance in Zeroth-order Optimization](https://mlsanity.com/paper/2206.07126/) (2022)
- [Zero-Order One-Point Estimate with Distributed Stochastic Gradient-Tracking Technique](https://mlsanity.com/paper/2210.05618/) (2022)
- [Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method](https://mlsanity.com/paper/2103.12954/) (2021)
- [SeedFlood: A Step Toward Scalable Decentralized Fine-Tuning of LLMs](https://mlsanity.com/paper/2602.18181/) (2026)
- [Communication Efficient and Privacy-Preserving Federated Learning Based on Evolution Strategies](https://mlsanity.com/paper/2311.03405/) (2023)
- [Asynchronous Message-Passing and Zeroth-Order Optimization Based Distributed Learning with a Use-Case in Resource Allocation in Communication Networks](https://mlsanity.com/paper/2311.04604/) (2023)
- [Distributed Online Bandit Nonconvex Optimization with One-Point Residual Feedback via Dynamic Regret](https://mlsanity.com/paper/2409.15680/) (2024)
- [A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis](https://mlsanity.com/paper/2603.12838/) (2026)

## Abstract (arXiv)

In this paper, we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.