# SpiderBoost and Momentum: Faster Stochastic Variance Reduction Algorithms

arXiv: https://arxiv.org/abs/1810.10690 · HTML: https://mlsanity.com/paper/1810.10690/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

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

- [Provably Faster Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2106.04692/) (2021)
- [Optimal Algorithms for Stochastic Multi-Level Compositional Optimization](https://mlsanity.com/paper/2202.07530/) (2022)
- [Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization](https://mlsanity.com/paper/2207.08540/) (2022)
- [Anchor Sampling for Federated Learning with Partial Client Participation](https://mlsanity.com/paper/2206.05891/) (2022)
- [Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2211.13668/) (2022)
- [ANITA: An Optimal Loopless Accelerated Variance-Reduced Gradient Method](https://mlsanity.com/paper/2103.11333/) (2021)
- [Lower Bounds and Proximally Anchored SGD for Non-Convex Minimization Under Unbounded Variance](https://mlsanity.com/paper/2604.16620/) (2026)
- [Beyond Bounded Variance: Variance-Reduced Normalized Methods for Nonconvex Optimization under Blum-Gladyshev Noise](https://mlsanity.com/paper/2605.15314/) (2026)
- [SYNTHESIS: A Semi-Asynchronous Path-Integrated Stochastic Gradient Method for Distributed Learning in Computing Clusters](https://mlsanity.com/paper/2208.08425/) (2022)
- [Zeroth-Order Stochastic Mirror Descent Algorithms for Minimax Excess Risk Optimization](https://mlsanity.com/paper/2408.12209/) (2024)
- [Grad Queue : A probabilistic framework to reinforce sparse gradients](https://mlsanity.com/paper/2404.16917/) (2024)

## Abstract (arXiv)

SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objective functions that involve nonsmooth regularizers. In this paper, we propose SpiderBoost as an improved scheme, which allows to use a much larger constant-level stepsize while maintaining the same near-optimal oracle complexity, and can be extended with proximal mapping to handle composite optimization (which is nonsmooth and nonconvex) with provable convergence guarantee. In particular, we show that proximal SpiderBoost achieves an oracle complexity of O(minn1/2ε-2,ε-3) in composite nonconvex optimization, improving the state-of-the-art result by a factor of O(minn1/6,ε-1/3). We further develop a novel momentum scheme to accelerate SpiderBoost for composite optimization, which achieves the near-optimal oracle complexity in theory and substantial improvement in experiments.