# On Biased Stochastic Gradient Estimation

arXiv: https://arxiv.org/abs/1906.01133 · HTML: https://mlsanity.com/paper/1906.01133/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 11 of 11)

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- [Improving the Straight-Through Estimator with Zeroth-Order Information](https://mlsanity.com/paper/2510.23926/) (2025)
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- [Parallel Momentum Methods Under Biased Gradient Estimations](https://mlsanity.com/paper/2403.00853/) (2024)
- [Accelerated Gradient Methods with Biased Gradient Estimates: Risk Sensitivity, High-Probability Guarantees, and Large Deviation Bounds](https://mlsanity.com/paper/2509.13628/) (2025)
- [BrowNNe: Brownian Nonlocal Neurons & Activation Functions](https://mlsanity.com/paper/2406.15617/) (2024)
- [Shuffling Gradient-Based Methods for Nonconvex-Concave Minimax Optimization](https://mlsanity.com/paper/2410.22297/) (2024)
- [DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing](https://mlsanity.com/paper/2510.18218/) (2025)
- [Descend or Rewind? Stochastic Gradient Descent Unlearning](https://mlsanity.com/paper/2511.15983/) (2025)
- [ABC-Align: Prediction-Powered Alignment with Adaptive Bias Control](https://mlsanity.com/paper/2609.34374/) (2026)
- [Generalization Analysis of Biased Stochastic Gradient Methods for Minimax Problems](https://mlsanity.com/paper/2610.19322/) (2026)

## Abstract (arXiv)

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we present allows us to extend proximal support to biased algorithms, including SAG and SARAH, for the first time in the convex setting. We also use our framework to develop a new algorithm, Stochastic Average Recursive GradiEnt (SARGE), that achieves the oracle complexity lower-bound for non-convex, finite-sum objectives and requires strictly fewer calls to a stochastic gradient oracle per iteration than SVRG and SARAH. We support our theoretical results with numerical experiments that demonstrate the benefits of certain biased gradient estimators.