Research map / Optimization / Optimizers
Stochastic gradient MCMC
Uses stochastic gradient Langevin dynamics and related samplers for scalable Bayesian posterior sampling.
142 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimizers, keyword cluster “variational · sampling · inference”
State History Tried Checklist 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.
24 papers in 2023–24 and 22 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 9.9% to 7.6%.
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 · Stochastic Optimization for Large-scale Optimal Transport (NeurIPS 2016 · 147 citations)
- 2017 · Deep Latent Dirichlet Allocation with Topic-Layer-Adaptive Stochastic Gradient Riemannian MCMC (ICML 2017 · 43 citations)
- 2018 · Not All Samples Are Created Equal: Deep Learning with Importance Sampling (ICML 2018 · 104 citations)
- 2019 · Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates (NeurIPS 2019 · 36 citations)
- 2020 · Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning (ICLR 2020 · 112 citations)
- 2021 · Sample Efficient Reinforcement Learning with REINFORCE (AAAI 2021 · 103 citations)
- 2022 · Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling (AAAI 2022 · 19 citations)
- 2023 · A Guide Through the Zoo of Biased SGD (NeurIPS 2023 · 4 citations)
- 2024 · On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design (AAAI 2024 · 3 citations)
- 2025 · Coupling-based Convergence Diagnostic and Stepsize Scheme for Stochastic Gradient Descent (AAAI 2025 · 1 citation)
- 2026 · SVRG and Beyond via Posterior Correction (ICML 2026 · 0 citations)
Earliest papers here
- Stochastic Optimization for Large-scale Optimal Transport (NeurIPS 2016 · 147 citations)
- A Variational Analysis of Stochastic Gradient Algorithms (ICML 2016 · 54 citations)
- Learning Weight Uncertainty With Stochastic Gradient MCMC for Shape Classification (CVPR 2016 · 43 citations)
What has been tried
125 papers here report 1,040 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 12%, hurt 14%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use an adaptive threshold that decreases with the stepsize rather than a static threshold | SGD stationarity detection · stationarity detection accuracy | Helped | Coupling-based Convergence Diagnostic and Stepsize Scheme for Stochastic Gradient Descent (AAAI 2025 · 1 citation) | |
| Use the dual rather than primal objective for gradient descent | UCI pol · convergence / K-norm error | 500× higher | Helped | Stochastic Gradient Descent for Gaussian Processes Done Right (ICLR 2024 · 1 citation) |
| Vary steps per cycle | MNIST, kMNIST, eMNIST, Omniglot, and Caltech · log MMD | Mixed | Gradient-based Discrete Sampling with Automatic Cyclical Scheduling (NeurIPS 2024 · 1 citation) | |
| Add regularization during RLNN training | MIS RB-[200--300] · set size | 18.64 -> 19.52 | Helped | Regularized Langevin Dynamics for Combinatorial Optimization (ICML 2025 · 0 citations) |
| add first-order gradient guidance | Linear chance constrained problem (n=8) · FvalMean | 0.3481 -> -0.6483 | Helped | A Gradient Guided Diffusion Framework for Chance Constrained Programming (NeurIPS 2025 · 0 citations) |
| Clip sampled values to [x_min, x_max] rather than using adaptive sampling | ImageNet, VGG16 · Sparseness | 0.5740(0.0000) vs 0.5294(0.0001) | Hurt | AdaptGrad: Adaptive Sampling to Reduce Noise (NeurIPS 2025 · 0 citations) |
| Set CG and LiSSA damping to 0.01 instead of 0.001 | Evaluated datasets · cosine similarity to further-training attribution | Helped | Final-Model-Only Data Attribution with a Unifying View of Gradient-Based Methods (NeurIPS 2025 · 0 citations) | |
| Use A-RFD asymptotic step sizes instead of the full RFD schedule | MNIST, batch size 1024 · validation loss | Hurt | Random Function Descent (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 13 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- CIFAR-10 · 3 of 13 papers
- MNIST · 2 of 13 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 46 papers; from OpenAlex and the papers' affiliations).
- University of Alberta · 3 papers
- IBM · 3 papers
- Cornell University · 2 papers
- University of Cambridge · 2 papers
- Purdue University · 2 papers
- Huazhong University of Science and Technology · 2 papers
- Microsoft · 2 papers
- ETHZ - ETH Zurich · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Natural gradient and Fisher approximations (77 papers)
- Stein variational gradient descent (47 papers)
- Zeroth-order training methods (23 papers)
Elsewhere in the topic
- Surrogate losses and robust solvers (119 papers)
- Differentiating through embedded optimization (117 papers)
- Constrained and non-backprop training (97 papers)
- Memory-efficient LLM optimizers (79 papers)
- Adam convergence and adaptive learning rates (78 papers)
- Randomized gradient estimation (77 papers)
- SGD momentum and step-size schedules (72 papers)
- Second-order and structured preconditioning (70 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).