# Learning efficient representations of complex constraints for scalable optimization

arXiv: https://arxiv.org/abs/2603.08283 · HTML: https://mlsanity.com/paper/2603.08283/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 79 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Learning Warm-Start Points for AC Optimal Power Flow](https://mlsanity.com/paper/1905.08860/) (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)
- [Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence](https://mlsanity.com/paper/1405.0766/) (2014)
- [Distributionally Robust Chance Constrained Data-enabled Predictive Control](https://mlsanity.com/paper/2006.01702/) (2020)
- [Free-Energy Machine for Combinatorial Optimization](https://mlsanity.com/paper/2412.09285/) (2024)
- [Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty under Wasserstein Ambiguity](https://mlsanity.com/paper/2003.12685/) (2020)
- [The Complexity of the Hausdorff Distance](https://mlsanity.com/paper/2112.04343/) (2021)
- [Learning Distribution Grid Topologies: A Tutorial](https://mlsanity.com/paper/2206.10837/) (2022)
- [Optimal Bound on the Combinatorial Complexity of Approximating Polytopes](https://mlsanity.com/paper/1910.14459/) (2019)
- [Explicit convex hull description of bivariate quadratic sets with indicator variables](https://mlsanity.com/paper/2208.08703/) (2022)
- [Aggregate Power Flexibility in Unbalanced Distribution Systems](https://mlsanity.com/paper/1812.05990/) (2018)
- [Convex Chance-Constrained Programs with Wasserstein Ambiguity](https://mlsanity.com/paper/2111.02486/) (2021)
- [Advancing Distributed AC Optimal Power Flow for Integrated Transmission-Distribution Systems](https://mlsanity.com/paper/2308.13282/) (2023)

## Abstract (arXiv)

Complex constraints often make real-world optimization computationally prohibitive at the scale and speed required for operational decision-making. Here we introduce PolyFormer, a PIML framework that learns compact polytopic representations of the geometry induced by complex constraints. PolyFormer captures constraint-induced geometry and transforms it into efficient polytopic reformulations, reducing the complexity of downstream optimization and enabling the use of off-the-shelf solvers. Neural parameterizations further enable rapid adaptation to varying operating conditions without retraining. Through evaluations across three important problems, i.e., large-scale resource aggregation, network-constrained optimization, and optimization under uncertainty, PolyFormer achieves online solver speedups of up to 6,400-fold and memory reductions of up to 99.87%, while maintaining small feasibility and objective errors. Together, these results establish learned geometric constraint representations as an effective and scalable route to prescriptive optimization under diverse forms of constraint complexity.