Research map / Optimization / Nonconvex and smooth optimization
Proximal finite-sum methods
Develops proximal and incremental stochastic methods for nonsmooth finite-sum problems.
47 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Nonconvex and smooth optimization, keyword cluster “variance · reduction · reduced”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
9 papers in 2023–24 and 7 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 2.8% to 2.0%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Variance Reduction for Faster Non-Convex Optimization (ICML 2016 · 119 citations)
- 2017 · Non-convex Finite-Sum Optimization Via SCSG Methods (NeurIPS 2017 · 129 citations)
- 2018 · A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization (NeurIPS 2018 · 66 citations)
- 2019 · A unified variance-reduced accelerated gradient method for convex optimization (NeurIPS 2019 · 31 citations)
- 2020 · A Catalyst Framework for Minimax Optimization (NeurIPS 2020 · 22 citations)
- 2021 · A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization (ICML 2021 · 7 citations)
- 2022 · RECAPP: Crafting a More Efficient Catalyst for Convex Optimization (ICML 2022 · 4 citations)
- 2023 · RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates (ICLR 2023 · 1 citation)
- 2024 · Decentralized Sum-of-Nonconvex Optimization (AAAI 2024 · 0 citations)
- 2025 · Faster Double Adaptive Gradient Methods (AAAI 2025 · 0 citations)
- 2026 · Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives (NeurIPS 2026 · 0 citations)
Earliest papers here
- Variance Reduction for Faster Non-Convex Optimization (ICML 2016 · 119 citations)
- Proximal Stochastic Methods for Nonsmooth Nonconvex Finite-Sum Optimization (NeurIPS 2016 · 107 citations)
- A Simple Practical Accelerated Method for Finite Sums (NeurIPS 2016 · 57 citations)
What has been tried
39 papers here report 235 measured changes (a component added, removed or swapped, compared with a baseline): helped 70%, no clear effect 14%, hurt 9%, mixed 7%. Papers mostly publish changes that helped, so "helped" is over-represented.
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 16 papers; from OpenAlex and the papers' affiliations).
- Fudan University · 3 papers
- KAUST · 2 papers
- King Abdullah University of Science and Technology · 2 papers
- EPFL · 2 papers
- University of Wisconsin - Madison · 2 papers
Use it
Download BibTeX of 32 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Stochastic variance reduction (86 papers)
- Variance-reduced policy gradient (17 papers)
Elsewhere in the topic
- Adaptive first-order convex methods (190 papers)
- Coordinate and Adam convergence analysis (188 papers)
- Stochastic gradient last-iterate analysis (178 papers)
- Nonconvex minimax and constrained methods (100 papers)
- Stochastic convex optimization complexity (94 papers)
- Acceleration and Nesterov dynamics (91 papers)
- Equilibrium learning in zero-sum games (88 papers)
- Complexity of nonconvex first-order methods (79 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).