mlsanityData to 7 Oct 2026

Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization

arXiv 1905.00529 ↗First posted 1 May 2019cs.LG math.OC stat.MLcited by 15

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Abstract (arXiv)

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an ε-second-order stationary point using only widetildeO(n2/3/ε2+n/ε1.5) stochastic gradients. To our best knowledge, this is the first second-order guarantee for a simple variant of SVRG. The running time almost matches the known guarantees for finding ε-first-order stationary points.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 May 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 4; 2023: 3; 2024: 0; 2025: 2; 2026: 1.

15 papers.

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  1. 2021ZeroSARAH: Efficient Nonconvex Finite-Sum Optimization with Zero Full Gradient Computationcited by 28
  2. 2021FedPAGE: A Fast Local Stochastic Gradient Method for Communication-Efficient Federated Learningcited by 19
  3. 2021Escape saddle points by a simple gradient-descent based algorithmcited by 11
  4. 2021ANITA: An Optimal Loopless Accelerated Variance-Reduced Gradient Methodcited by 9
  5. 2023Regret-Optimal Model-Free Reinforcement Learning for Discounted MDPs with Short Burn-In Timecited by 8
  6. 2025Unbiased Gradient Low-Rank Projectioncited by 6
  7. 2022Simple and Optimal Stochastic Gradient Methods for Nonsmooth Nonconvex Optimizationcited by 5
  8. 2023Escaping Saddle Points in Heterogeneous Federated Learning via Distributed SGD with Communication Compressioncited by 4
  9. 2025Second-Order Convergence in Private Stochastic Non-Convex Optimizationcited by 3
  10. 2022Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learningcited by 2
  11. 2021Distributed Policy Gradient with Variance Reduction in Multi-Agent Reinforcement Learningcited by 1
  12. 2023Greedy Pruning with Group Lasso Provably Generalizes for Matrix Sensingcited by 1
3 more
  1. 2026AdaCubic: An Adaptive Cubic Regularization Optimizer for Deep Learningcited by 1
  2. 2022SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimizationcited by 0
  3. 2022Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learningcited by 0