# Neural Operators for Multi-Task Control and Adaptation

arXiv: https://arxiv.org/abs/2604.03449 · HTML: https://mlsanity.com/paper/2604.03449/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 30 of 33)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Efficient Off-Policy Meta-Reinforcement Learning via Probabilistic Context Variables](https://mlsanity.com/paper/1903.08254/) (2019)
- [Distral: Robust Multitask Reinforcement Learning](https://mlsanity.com/paper/1707.04175/) (2017)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Multi-Task Reinforcement Learning with Context-based Representations](https://mlsanity.com/paper/2102.06177/) (2021)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Meta reinforcement learning as task inference](https://mlsanity.com/paper/1905.06424/) (2019)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [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)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations](https://mlsanity.com/paper/2212.04663/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Policy Architectures for Compositional Generalization in Control](https://mlsanity.com/paper/2203.05960/) (2022)
- [D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators](https://mlsanity.com/paper/2310.18888/) (2023)
- [Meta Reinforcement Learning with Task Embedding and Shared Policy](https://mlsanity.com/paper/1905.06527/) (2019)
- [PolyTask: Learning Unified Policies through Behavior Distillation](https://mlsanity.com/paper/2310.08573/) (2023)
- [Exchangeable Input Representations for Reinforcement Learning](https://mlsanity.com/paper/2003.09022/) (2020)
- [Comparing the Efficacy of Fine-Tuning and Meta-Learning for Few-Shot Policy Imitation](https://mlsanity.com/paper/2306.13554/) (2023)
- [Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations](https://mlsanity.com/paper/2401.15482/) (2024)

## Built on by (most cited first, 1 of 1)

- [Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers](https://mlsanity.com/paper/2606.09047/) (2026)

## Abstract (arXiv)

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.