Research map / Learning theory and algorithms / Combinatorial and search optimization
Predict-then-optimize learning
Trains predictors with downstream linear or integer programs, including solver-free and multi-stage objectives.
89 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Combinatorial and search optimization, keyword cluster “integer · linear · mixed”
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.
26 papers in 2023–24 and 18 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 7.5% to 5.0%.
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 · Large-Scale Price Optimization via Network Flow (NeurIPS 2016 · 25 citations)
- 2017 · DeepCoder: Learning to Write Programs (ICLR 2017 · 217 citations)
- 2018 · Differentiable Dynamic Programming for Structured Prediction and Attention (ICML 2018 · 78 citations)
- 2019 · Learning Optimal Classification Trees Using a Binary Linear Program Formulation (AAAI 2019 · 141 citations)
- 2020 · Interior Point Solving for LP-based prediction+optimisation (NeurIPS 2020 · 42 citations)
- 2021 · A Scalable Two Stage Approach to Computing Optimal Decision Sets (AAAI 2021 · 17 citations)
- 2022 · Neur2SP: Neural Two-Stage Stochastic Programming (NeurIPS 2022 · 11 citations)
- 2023 · Necessary and Sufficient Conditions for Optimal Decision Trees using Dynamic Programming (NeurIPS 2023 · 2 citations)
- 2024 · Optimal Survival Trees: A Dynamic Programming Approach (AAAI 2024 · 7 citations)
- 2025 · Learning Valid Dual Bounds in Constraint Programming: Boosted Lagrangian Decomposition with Self-Supervised Learning (AAAI 2025 · 1 citation)
- 2026 · Learning to Approximate Uniform Facility Location via Graph Neural Networks (ICML 2026 · 0 citations)
Earliest papers here
- Large-Scale Price Optimization via Network Flow (NeurIPS 2016 · 25 citations)
- SDP Relaxation with Randomized Rounding for Energy Disaggregation (NeurIPS 2016 · 22 citations)
- Assortment Optimization Under the Mallows model (NeurIPS 2016 · 16 citations)
What has been tried
73 papers here report 622 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 8%, hurt 20%, 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 the specialized depth-two solver | Runtime on evaluated datasets · runtime reduction | 45 times | Helped | Optimal Survival Trees: A Dynamic Programming Approach (AAAI 2024 · 7 citations) |
| remove GNN message passing and use MLP predictors only | Graph matching · g_I | 0.19 -> 0.42 | Hurt | DOGE-Train: Discrete Optimization on GPU with End-to-End Training (AAAI 2024 · 3 citations) |
| Remove local steepest-edge information from EXP | NETLIB subset · geometric mean of pivot numbers | 112 -> 139 | Hurt | Learning to Pivot as a Smart Expert (AAAI 2024 · 3 citations) |
| replace FNO with MLP | Darcy Flow, matrix size 32400 · principal angle (rad) | 0.07 -> 0.54 | Hurt | Neural Krylov Iteration for Accelerating Linear System Solving (NeurIPS 2024 · 3 citations) |
| Replace sub-gradient optimization with learned bounds at every search node | MKP, 50 items · time (sec.) | 158 to 36 | Helped | Learning Valid Dual Bounds in Constraint Programming: Boosted Lagrangian Decomposition with Self-Supervised Learning (AAAI 2025 · 1 citation) |
| add neighborhood pruning | Depth 2 · D2Split calls pruned | 91.1% | Helped | Optimal Classification Trees for Continuous Feature Data Using Dynamic Programming with Branch-and-Bound (AAAI 2025 · 1 citation) |
| Use FFNN rather than GCN to predict dual variables | GCB graphs · MSE | 0.059 -> 0.038 | Helped | Adaptive Stabilization Based on Machine Learning for Column Generation (ICML 2024 · 1 citation) |
| use adaptive rather than linear penalty updates | KG-sym 250 · true rel error | 5.32% -> 3.91% | Helped | Learning Generalized Linear Programming Value Functions (NeurIPS 2024 · 1 citation) |
| Increase the simplex primitive dimension from p=3 to p=6 | 5-node power system test · predictability loss ℓθp / ℓp | 3.20 -> 1.91 | Helped | Inverse Optimization via Learning Feasible Regions (ICML 2025 · 0 citations) |
| Use closed-loop rather than open-loop policies | Centralized QPs · iterations to desired accuracy | Helped | Deep Distributed Optimization for Large-Scale Quadratic Programming (ICLR 2025 · 0 citations) | |
| Generate CG cut parameters with a linear-threshold neural network instead of the RL approach | 1,000 novel test instances from the Chvátal distribution · average tree size | Mixed | Sample Complexity of Algorithm Selection Using Neural Networks and Its Applications to Branch-and-Cut (NeurIPS 2024 · 0 citations) | |
| Train on varied-size LPs instead of fixed-size LPs | Packing, MaxFlow, and MinCostFlow with varied test sizes · objective ratio | Helped | Learning to Generate Projections for Reducing Dimensionality of Heterogeneous Linear Programming Problems (ICML 2025) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 44 papers; from OpenAlex and the papers' affiliations).
- Delft University of Technology · 6 papers
- The Chinese University of Hong Kong · 4 papers
- Stanford University · 3 papers
- University of Toronto · 2 papers
- Shanghai University of Finance and Economics · 2 papers
- Royal Melbourne Institute of Technology · 2 papers
- La Trobe University · 2 papers
- Monash University · 2 papers
- Shenzhen Research Institute of Big Data · 2 papers
- Department of Computer Science and Engineering · 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
- Heuristics for integer programming (60 papers)
- Learning branch-and-cut for MILP (54 papers)
- Semidefinite relaxations for verification (47 papers)
Elsewhere in the topic
- Logic and answer set programming theory (150 papers)
- Heuristic and local search algorithms (147 papers)
- Classical and HTN planning (145 papers)
- Unsupervised neural combinatorial optimization (113 papers)
- Constrained neural network optimization (111 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
- Structure and complexity of constraint reasoning (92 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).