# Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems

arXiv: https://arxiv.org/abs/2509.18404 · HTML: https://mlsanity.com/paper/2509.18404/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 25 of 25)

- [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)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [A mean-field games laboratory for generative modeling](https://mlsanity.com/paper/2304.13534/) (2023)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding](https://mlsanity.com/paper/2104.03270/) (2021)
- [Basis-to-Basis Operator Learning Using Function Encoders](https://mlsanity.com/paper/2410.00171/) (2024)
- [A Neural Network Architecture to Learn Explicit MPC Controllers from Data](https://mlsanity.com/paper/1911.10789/) (2019)
- [A Neural Network Approach for Stochastic Optimal Control](https://mlsanity.com/paper/2209.13104/) (2022)
- [Function Encoders: A Principled Approach to Transfer Learning in Hilbert Spaces](https://mlsanity.com/paper/2501.18373/) (2025)
- [Neural Network Approaches for Parameterized Optimal Control](https://mlsanity.com/paper/2402.10033/) (2024)
- [Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiency](https://mlsanity.com/paper/2505.13499/) (2025)
- [Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics](https://mlsanity.com/paper/2303.04569/) (2023)

## Built on by (most cited first, 2 of 2)

- [Neural Operators for Multi-Task Control and Adaptation](https://mlsanity.com/paper/2604.03449/) (2026)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)

## Abstract (arXiv)

This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting in prohibitive computational costs for applications requiring frequent evaluation and adaptation. The proposed method learns a reusable set of neural basis functions that spans the control policy space, enabling efficient zero-shot adaptation to new tasks through either projection from data or direct mapping from problem specifications. The key idea is an offline-online decomposition: basis functions are learned once during offline imitation learning, while online adaptation requires only lightweight coefficient estimation. Numerical experiments across diverse dynamics, dimensions, and cost structures show our method delivers near-optimal performance with minimal overhead when generalizing across tasks, enabling semi-global feedback policies suitable for real-time deployment.