# Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method

arXiv: https://arxiv.org/abs/2103.12954 · HTML: https://mlsanity.com/paper/2103.12954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 24 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [Improved Zeroth-Order Variance Reduced Algorithms and Analysis for Nonconvex Optimization](https://mlsanity.com/paper/1910.12166/) (2019)
- [A Comprehensive Linear Speedup Analysis for Asynchronous Stochastic Parallel Optimization from Zeroth-Order to First-Order](https://mlsanity.com/paper/1606.00498/) (2016)
- [Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points](https://mlsanity.com/paper/1809.06474/) (2018)
- [Zeroth Order Nonconvex Multi-Agent Optimization over Networks](https://mlsanity.com/paper/1710.09997/) (2017)
- [Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization](https://mlsanity.com/paper/1903.04157/) (2019)
- [Distributed Zero-Order Algorithms for Nonconvex Multi-Agent Optimization](https://mlsanity.com/paper/1908.11444/) (2019)
- [Derivative-Free Method For Composite Optimization With Applications To Decentralized Distributed Optimization](https://mlsanity.com/paper/1911.10645/) (2019)
- [Distributed Optimization for Second-Order Multi-Agent Systems with Dynamic Event-Triggered Communication](https://mlsanity.com/paper/1803.06380/) (2018)
- [Distributed Zeroth Order Optimization Over Random Networks: A Kiefer-Wolfowitz Stochastic Approximation Approach](https://mlsanity.com/paper/1803.07844/) (2018)
- [Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework](https://mlsanity.com/paper/2012.11518/) (2020)

## Built on by (most cited first, 1 of 1)

- [Heterogeneous Federated Learning with Splited Language Model](https://mlsanity.com/paper/2403.16050/) (2024)

## Abstract (arXiv)

This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of n local cost functions. We solve such a problem by involving zeroth-order (ZO) information exchange. In this paper, we propose a ZO distributed primal-dual coordinate method (ZODIAC) to solve the stochastic optimization problem. Agents approximate their own local stochastic ZO oracle along with coordinates with an adaptive smoothing parameter. We show that the proposed algorithm achieves the convergence rate of O(√p/√T) for general nonconvex cost functions. We demonstrate the efficiency of proposed algorithms through a numerical example in comparison with the existing state-of-the-art centralized and distributed ZO algorithms.