# An Accelerated DFO Algorithm for Finite-sum Convex Functions

arXiv: https://arxiv.org/abs/2007.03311 · HTML: https://mlsanity.com/paper/2007.03311/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

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

- [On the Second-order Convergence Properties of Random Search Methods](https://mlsanity.com/paper/2110.13265/) (2021)
- [An Accelerated Variance-Reduced Conditional Gradient Sliding Algorithm for First-order and Zeroth-order Optimization](https://mlsanity.com/paper/2109.08858/) (2021)
- [Stochastic Two Points Method for Deep Model Zeroth-order Optimization](https://mlsanity.com/paper/2402.01621/) (2024)
- [Obtaining Lower Query Complexities through Lightweight Zeroth-Order Proximal Gradient Algorithms](https://mlsanity.com/paper/2410.02559/) (2024)

## Abstract (arXiv)

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given to the concept of acceleration in the DFO literature, existing stochastic algorithms for objective functions with a finite-sum structure have not been shown theoretically to achieve an accelerated rate of convergence. Algorithms that use acceleration in such a setting are prone to instabilities, making it difficult to reach convergence. In this work, we exploit the finite-sum structure of the objective in order to design a variance-reduced DFO algorithm that provably yields acceleration. We prove rates of convergence for both smooth convex and strongly-convex finite-sum objective functions. Finally, we validate our theoretical results empirically on several tasks and datasets.