# A Historical Trajectory Assisted Optimization Method for Zeroth-Order Federated Learning

arXiv: https://arxiv.org/abs/2409.15955 · HTML: https://mlsanity.com/paper/2409.15955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 24 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [FedPrompt: Communication-Efficient and Privacy Preserving Prompt Tuning in Federated Learning](https://mlsanity.com/paper/2208.12268/) (2022)
- [Tackling System and Statistical Heterogeneity for Federated Learning with Adaptive Client Sampling](https://mlsanity.com/paper/2112.11256/) (2021)
- [Federated Learning of Large Language Models with Parameter-Efficient Prompt Tuning and Adaptive Optimization](https://mlsanity.com/paper/2310.15080/) (2023)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [FedBPT: Efficient Federated Black-box Prompt Tuning for Large Language Models](https://mlsanity.com/paper/2310.01467/) (2023)
- [Generalizing Gaussian Smoothing for Random Search](https://mlsanity.com/paper/2211.14721/) (2022)
- [Hessian-Aware Zeroth-Order Optimization for Black-Box Adversarial Attack](https://mlsanity.com/paper/1812.11377/) (2018)
- [Federated Zeroth-Order Optimization using Trajectory-Informed Surrogate Gradients](https://mlsanity.com/paper/2308.04077/) (2023)
- [Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients](https://mlsanity.com/paper/2210.01496/) (2022)
- [Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization](https://mlsanity.com/paper/2109.12213/) (2021)
- [FedZeN: Towards superlinear zeroth-order federated learning via incremental Hessian estimation](https://mlsanity.com/paper/2309.17174/) (2023)

## Abstract (arXiv)

Federated learning heavily relies on distributed gradient descent techniques. In the situation where gradient information is not available, the gradients need to be estimated from zeroth-order information, which typically involves computing finite-differences along isotropic random directions. This method suffers from high estimation errors, as the geometric features of the objective landscape may be overlooked during the isotropic sampling. In this work, we propose a non-isotropic sampling method to improve the gradient estimation procedure. Gradients in our method are estimated in a subspace spanned by historical trajectories of solutions, aiming to encourage the exploration of promising regions and hence improve the convergence. The proposed method uses a covariance matrix for sampling which is a convex combination of two parts. The first part is a thin projection matrix containing the basis of the subspace which is designed to improve the exploitation ability. The second part is the historical trajectories. We implement this method in zeroth-order federated settings, and show that the convergence rate aligns with existing ones while introducing no significant overheads in communication or local computation. The effectiveness of our proposal is verified on several numerical experiments in comparison to several commonly-used zeroth-order federated optimization algorithms.