# A Scalable Learned Iterative Solver for Nonlinear MPC via Temporal Decomposition

arXiv: https://arxiv.org/abs/2610.13480 · HTML: https://mlsanity.com/paper/2610.13480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
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- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
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- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming](https://mlsanity.com/paper/2406.01908/) (2024)
- [Probabilistic performance validation of deep learning-based robust NMPC controllers](https://mlsanity.com/paper/1910.13906/) (2019)
- [Learning Algorithm Hyperparameters for Fast Parametric Convex Optimization](https://mlsanity.com/paper/2411.15717/) (2024)
- [Optimal Deterministic Algorithm Generation](https://mlsanity.com/paper/1609.06917/) (2016)
- [FBstab: A Stabilized Semismooth Quadratic Programming Algorithm with Applications in Model Predictive Control](https://mlsanity.com/paper/1901.04046/) (2019)
- [A Regularized and Smoothed Fischer-Burmeister Method for Quadratic Programming with Applications to Model Predictive Control](https://mlsanity.com/paper/1807.03214/) (2018)
- [Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs](https://mlsanity.com/paper/2101.03067/) (2021)
- [Self-Supervised Learning of Iterative Solvers for Constrained Optimization](https://mlsanity.com/paper/2409.08066/) (2024)
- [Superconvergence of Online Optimization for Model Predictive Control](https://mlsanity.com/paper/2001.03707/) (2020)
- [Robust Model Predictive Control Exploiting Monotonicity Properties](https://mlsanity.com/paper/2408.17348/) (2024)

## Abstract (arXiv)

Nonlinear model predictive control (NMPC) can be applied to large nonlinear systems with complex objectives while enforcing constraints, but the cost of solving the underlying optimization problems limits real-time application for systems with fast dynamics or many states. Neural networks can reduce this online cost by approximating the control law, but may violate constraints and typically require many precomputed optimizer solutions for training. The learning-based iterative solver for constrained optimization (LISCO) instead learns to predict primal-dual steps toward satisfaction of the Karush-Kuhn-Tucker (KKT) conditions through self-supervised training without precomputed solutions, but its dense, monolithic architecture grows with the prediction horizon. We remove this horizon dependence by exploiting the temporal structure of the problem in the solver architecture, which makes the network size independent of the horizon while leaving the training loss and the solver iteration unchanged. A closed-loop resampling strategy further aligns the training distribution with closed-loop operation at no additional sampling cost. On an economic NMPC benchmark of a CSTR cascade, the proposed solver scales to larger problems than monolithic LISCO and achieves median speedups of up to a factor of four over IPOPT. In closed loop, it achieves comparable control performance to IPOPT with no observed constraint violations.