# Global Convergence and Acceleration for Single Observation Gradient Free Optimization

arXiv: https://arxiv.org/abs/2509.04424 · HTML: https://mlsanity.com/paper/2509.04424/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2025.

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

- [Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Cooling](https://mlsanity.com/paper/2609.06196/) (2026)

## Abstract (arXiv)

Simultaneous perturbation stochastic approximation (SPSA) is an approach to gradient-free optimization introduced by Spall as a simplification of the approach of Kiefer and Wolfowitz. In many cases the most attractive option is the single-sample version known as 1SPSA, which is the focus of the present paper, containing two major contributions: a modification of the algorithm designed to ensure convergence from arbitrary initial condition, and a new approach to exploration to dramatically accelerate the rate of convergence. Examples are provided to illustrate the theory, and to demonstrate that estimates from unmodified 1SPSA may diverge even for a quadratic objective function.