Research map / Optimization / Optimizers
Differentiating through embedded optimization
Backpropagates through optimization layers and learns optimizers or proximal operators.
117 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Optimizers, keyword cluster “differentiable · functions · loss”
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.
33 papers in 2023–24 and 31 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 13.6% to 10.7%.
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 · The Parallel Knowledge Gradient Method for Batch Bayesian Optimization (NeurIPS 2016 · 121 citations)
- 2017 · Learning to Learn without Gradient Descent by Gradient Descent (ICML 2017 · 174 citations)
- 2018 · DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems (CVPR 2018 · 41 citations)
- 2019 · Stochastic Optimization of Sorting Networks via Continuous Relaxations (ICLR 2019 · 73 citations)
- 2020 · Auto-Tuning Structured Light by Optical Stochastic Gradient Descent (CVPR 2020 · 27 citations)
- 2021 · On the Verification of Neural ODEs with Stochastic Guarantees (AAAI 2021 · 17 citations)
- 2022 · Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games (AAAI 2022 · 13 citations)
- 2023 · Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances (NeurIPS 2023 · 4 citations)
- 2024 · Gradient Guidance for Diffusion Models: An Optimization Perspective (NeurIPS 2024 · 4 citations)
- 2025 · Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems (AAAI 2025 · 2 citations)
- 2026 · Towards Efficient LLMs Annealing with Principled Sample Selection (ICML 2026 · 0 citations)
Earliest papers here
- The Parallel Knowledge Gradient Method for Batch Bayesian Optimization (NeurIPS 2016 · 121 citations)
- Sublabel-Accurate Relaxation of Nonconvex Energies (CVPR 2016 · 39 citations)
- Regularized Nonlinear Acceleration (NeurIPS 2016 · 39 citations)
What has been tried
91 papers here report 803 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 10%, hurt 18%, 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 |
|---|---|---|---|---|
| Add SPM to DAN | SD3 20×10, greedy · Obj | 1376.18 -> 1289.77 | Helped | Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems (AAAI 2025 · 2 citations) |
| Use too large or too small perturbation amplitude rho | PACS and OfficeHome · accuracy | Hurt | Domain-Inspired Sharpness-Aware Minimization Under Domain Shifts (ICLR 2024 · 2 citations) | |
| Use Taylor-corrected ECCD instead of BCD at s=32 | duke, λ=0.001, s=32 · relative objective difference | 5.79 \times \text{10}^{\text{10}} -> 4.20\times10^{-7} | Helped | Enhanced Cyclic Coordinate Descent Methods for Elastic Net Penalized Linear Models (NeurIPS 2025 · 1 citation) |
| track 10 feasibility-seeking iterations instead of none during backpropagation | Convex QP, n=100 · optimality gap (%) | 14.143\std{0.024} -> 0.015\std{0.001} | Helped | FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees (NeurIPS 2025 · 1 citation) |
| Use greedy selection at Γ=0.75 instead of the no-surrogate baseline | Inventory Management Problem · average convergence speed | 19.43% faster | Helped | Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates (AAAI 2024 · 1 citation) |
| Vary the submanifold dimension r | PCA · performance robustness | No clear effect | Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method (ICML 2025 · 0 citations) | |
| Remove reference inputs (R-VF w/o ref) | Microreactor2D · relative-l2 error (p) | 1.33e-2 -> 5.56e-2 | Hurt | Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators (ICML 2025 · 0 citations) |
| add the MC term to the quadratic objective | SATLIB · MIS size | nearly 11 nodes | Helped | Differentiable Quadratic Optimization For the Maximum Independent Set Problem (ICML 2025 · 0 citations) |
| remove memory | robotic control environments · performance | 42-58% performance decrease | Hurt | Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains (NeurIPS 2025 · 0 citations) |
| use SAI loss instead of L2 or cosine similarity loss | Heat, Poisson, Hyperelasticity, and Synthetic · average CG iterations | Heat: 195.6 / 207.3 / 197.4; Poisson: 134.1 / 133.4 / 128.8; Hyperelasticity: 185.4 / 182.5 / 175.7; Synthetic: 2109.8 / | Mixed | Learning Sparse Approximate Inverse Preconditioners for Conjugate Gradient Solvers on GPUs (NeurIPS 2025 · 0 citations) |
| Replace regular BPTT with the modified update (stop feedback through the network from its output to its input) | Guidance-by-Repulsion hyperparameter study · best-run loss | 0.590 -> 0.465 | Helped | Stabilizing Backpropagation Through Time to Learn Complex Physics (ICLR 2024 · 0 citations) |
| Increase κp in νPI | CIFAR-10 global sparsity · overshoot | Mixed | On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization (ICML 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 64 papers; from OpenAlex and the papers' affiliations).
- Princeton University · 4 papers
- Massachusetts Institute of Technology · 4 papers
- Tsinghua University · 4 papers
- Stanford University · 3 papers
- University of Cambridge · 2 papers
- University of Michigan - Ann Arbor · 2 papers
- Shanghai Jiao Tong University · 2 papers
- Georgia Institute of Technology · 2 papers
- University of Illinois, Urbana Champaign · 2 papers
- The University of Tokyo · 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
- Surrogate losses and robust solvers (119 papers)
- Constrained and non-backprop training (97 papers)
- Randomized gradient estimation (77 papers)
- Multi-objective gradient methods (28 papers)
Elsewhere in the topic
- Stochastic gradient MCMC (142 papers)
- Memory-efficient LLM optimizers (79 papers)
- Adam convergence and adaptive learning rates (78 papers)
- Natural gradient and Fisher approximations (77 papers)
- SGD momentum and step-size schedules (72 papers)
- Second-order and structured preconditioning (70 papers)
- Stein variational gradient descent (47 papers)
- Gradient-based meta-learning theory (40 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).