# DCEmbed: Scalable Optimization over Neural Surrogates

arXiv: https://arxiv.org/abs/2609.33879 · HTML: https://mlsanity.com/paper/2609.33879/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Partition-based formulations for mixed-integer optimization of trained ReLU neural networks](https://mlsanity.com/paper/2102.04373/) (2021)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [OMLT: Optimization & Machine Learning Toolkit](https://mlsanity.com/paper/2202.02414/) (2022)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [Scaling Mixed-Integer Programming for Certification of Neural Network Controllers Using Bounds Tightening](https://mlsanity.com/paper/2403.17874/) (2024)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [Optimization over Trained Neural Networks: Difference-of-Convex Algorithm and Application to Data Center Scheduling](https://mlsanity.com/paper/2503.17506/) (2025)
- [Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial](https://mlsanity.com/paper/2605.26577/) (2026)

## Abstract (arXiv)

Neural surrogates can accelerate large-scale optimization by replacing expensive or intractable model components with efficient learned approximations, but solving the resulting embedded problems can remain prohibitively costly. For instance, standard exact encodings of neural networks with ReLU activations allow the problem to be solved by mixed-integer solvers, but add large numbers of binary variables to accommodate the nonlinearity of the activations, which can render the problem computationally prohibitive. To address this, we propose DCEmbed, a heuristic for optimization problems with embedded neural surrogates that leverages the difference-of-convex (DC) representation of the network and avoids adding activation binaries. Exploiting shared structure within the DC representation of a ReLU network, we derive a reduced-size, exact formulation for its convex components that can be embedded in optimization problems using just two linear inequalities and one continuous auxiliary variable per hidden neuron. Using this, the problem is solved via an iterative penalty convex-concave procedure, where only the concave portions of the neural terms are approximated at each stage. The original objective, constraints, and any discrete decisions are retained, allowing standard convex or mixed-integer optimization solvers to optimize the host and surrogate jointly at each iteration. In experiments on quadratic programs, mixed-integer resource allocation, and neural two-stage stochastic programming, our method demonstrates much faster progress toward high-quality feasible solutions than approaches using exact mixed-integer embeddings. In particular, DCEmbed achieves 4× lower normalized primal integral than the best exact baseline on the resource allocation problem, while in two-stage stochastic programming it reaches the global surrogate optimum ~ 5× faster than Gurobi ML.