# Generalized Simultaneous Perturbation-based Gradient Search with Reduced Estimator Bias

arXiv: https://arxiv.org/abs/2212.10477 · HTML: https://mlsanity.com/paper/2212.10477/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2022.

## Built on by (most cited first, 3 of 3)

- [Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications](https://mlsanity.com/paper/2312.02828/) (2023)
- [Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updating](https://mlsanity.com/paper/2303.16241/) (2023)
- [Generalized Random Direction Newton Algorithms for Stochastic Optimization](https://mlsanity.com/paper/2602.19893/) (2026)

## Abstract (arXiv)

We present in this paper a family of generalized simultaneous perturbation-based gradient search (GSPGS) estimators that use noisy function measurements. The number of function measurements required by each estimator is guided by the desired level of accuracy. We first present in detail unbalanced generalized simultaneous perturbation stochastic approximation (GSPSA) estimators and later present the balanced versions (B-GSPSA) of these. We extend this idea further and present the generalized smoothed functional (GSF) and generalized random directions stochastic approximation (GRDSA) estimators, respectively, as well as their balanced variants. We show that estimators within any specified class requiring more number of function measurements result in lower estimator bias. We present a detailed analysis of both the asymptotic and non-asymptotic convergence of the resulting stochastic approximation schemes. We further present a series of experimental results with the various GSPGS estimators on the Rastrigin and quadratic function objectives. Our experiments are seen to validate our theoretical findings.