Research map / Optimization / Nonconvex and smooth optimization
Langevin sampling for nonconvex problems
Analyzes Langevin and mirror-Langevin dynamics for sampling and noisy SGD in nonconvex settings.
70 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in Nonconvex and smooth optimization, keyword cluster “coordinate · proximal · bounds”
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.
14 papers in 2023–24 and 25 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.4% to 7.1%.
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
- 2018 · Global Non-convex Optimization with Discretized Diffusions (NeurIPS 2018 · 8 citations)
- 2019 · Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices (NeurIPS 2019 · 31 citations)
- 2020 · Continuous Regularized Wasserstein Barycenters (NeurIPS 2020 · 16 citations)
- 2021 · Non-asymptotic convergence bounds for Wasserstein approximation using point clouds (NeurIPS 2021 · 8 citations)
- 2022 · Bregman Proximal Langevin Monte Carlo via Bregman-Moreau Envelopes (ICML 2022 · 0 citations)
- 2023 · Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates (AAAI 2023 · 1 citation)
- 2024 · In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies (NeurIPS 2024 · 4 citations)
- 2025 · Convergence Rate in a Nonlinear Two-Time-Scale Stochastic Approximation with State (Time)-Dependence (AAAI 2025 · 1 citation)
- 2026 · DC-LA: Difference-of-Convex Langevin Algorithm (ICML 2026 · 0 citations)
Earliest papers here
- Global Non-convex Optimization with Discretized Diffusions (NeurIPS 2018 · 8 citations)
- Gen-Oja: Simple & Efficient Algorithm for Streaming Generalized Eigenvector Computation (NeurIPS 2018 · 5 citations)
- Continuous Relaxation of MAP Inference: A Nonconvex Perspective (CVPR 2018 · 3 citations)
What has been tried
50 papers here report 247 measured changes (a component added, removed or swapped, compared with a baseline): helped 72%, no clear effect 9%, hurt 10%, mixed 9%. 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 39 papers; from OpenAlex and the papers' affiliations).
- The University of Tokyo · 3 papers
- University of Toronto · 3 papers
- University of Oxford · 2 papers
- EPFL · 2 papers
- Kyushu Institute of Technology · 2 papers
- A*STAR · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Adaptive first-order convex methods (190 papers)
- Stochastic gradient last-iterate analysis (178 papers)
- Coordinate and Adam convergence analysis (188 papers)
- Acceleration and Nesterov dynamics (91 papers)
Elsewhere in the topic
- Nonconvex minimax and constrained methods (100 papers)
- Stochastic convex optimization complexity (94 papers)
- Equilibrium learning in zero-sum games (88 papers)
- Stochastic variance reduction (86 papers)
- Complexity of nonconvex first-order methods (79 papers)
- Penalty and implicit-gradient bilevel methods (65 papers)
- Proximal finite-sum methods (47 papers)
- Stochastic Frank-Wolfe methods (43 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).