# Enhanced Derivative-Free Optimization Using Adaptive Correlation-Induced Finite Difference Estimators

arXiv: https://arxiv.org/abs/2502.20819 · HTML: https://mlsanity.com/paper/2502.20819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [A Progressive Batching L-BFGS Method for Machine Learning](https://mlsanity.com/paper/1802.05374/) (2018)
- [ASTRO-DF: A Class of Adaptive Sampling Trust-Region Algorithms for Derivative-Free Stochastic Optimization](https://mlsanity.com/paper/1610.06506/) (2016)
- [Derivative-Free Optimization of Noisy Functions via Quasi-Newton Methods](https://mlsanity.com/paper/1803.10173/) (2018)
- [Surrogate-Based Simulation Optimization](https://mlsanity.com/paper/2105.03893/) (2021)
- [Derivative-Free Optimization via Adaptive Sampling Strategies](https://mlsanity.com/paper/2404.11893/) (2024)
- [A Correlation-induced Finite Difference Estimator](https://mlsanity.com/paper/2405.05638/) (2024)

## Abstract (arXiv)

Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA), typically utilize only two samples per iteration, resulting in imprecise gradient estimates and necessitating diminishing step sizes for convergence. In this paper, we first explore an efficient FD estimate, referred to as correlation-induced FD estimate, which is a batch-based estimate. Then, we propose an adaptive sampling strategy that dynamically determines the batch size at each iteration. By combining these two components, we develop an algorithm designed to enhance DFO in terms of both gradient estimation efficiency and sample efficiency. Furthermore, we establish the consistency of our proposed algorithm and demonstrate that, despite using a batch of samples per iteration, it achieves the same convergence rate as the KW and SPSA methods. Additionally, we propose a novel stochastic line search technique to adaptively tune the step size in practice. Finally, comprehensive numerical experiments confirm the superior empirical performance of the proposed algorithm.