Academic

Neural Operators for Multi-Task Control and Adaptation

arXiv:2604.03449v1 Announce Type: new Abstract: 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 ligh

D
David Sewell, Xingjian Li, Stepan Tretiakov, Krishna Kumar, David Fridovich-Keil · · 1 min read · 13 views
#cs.LG #cs.SY #eess.SY

arXiv:2604.03449v1 Announce Type: new Abstract: 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.

Executive Summary

This article introduces neural operators as a powerful tool for multi-task control and adaptation problems. The authors propose a permutation-invariant neural operator architecture that can learn mappings between infinite-dimensional function spaces. A single operator trained via behavioral cloning can accurately approximate the solution operator and generalize to unseen tasks, out-of-distribution settings, and varying amounts of task observations. The branch-trunk structure of the neural operator architecture enables efficient and flexible adaptation to new tasks. The authors also develop structured adaptation strategies and meta-trained operator variants that optimize the initialization for few-shot adaptation. The results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.

Key Points

  • ▸ Neural operators can learn mappings between infinite-dimensional function spaces.
  • ▸ The authors propose a permutation-invariant neural operator architecture for multi-task control problems.
  • ▸ A single operator trained via behavioral cloning can generalize to unseen tasks and out-of-distribution settings.

Merits

Strength in Generalization

The proposed neural operator architecture demonstrates strong generalization capabilities, achieving accurate results across various tasks and environments.

Efficient Adaptation

The branch-trunk structure of the neural operator architecture enables efficient and flexible adaptation to new tasks, making it suitable for real-world applications.

Demerits

Limited Exploration of Applications

The article focuses on multi-task control problems, and further exploration of the neural operator framework in other areas, such as reinforcement learning or computer vision, would be beneficial.

Lack of Comparative Analysis

A more comprehensive comparison with existing methods, such as traditional reinforcement learning or meta-learning techniques, would strengthen the argument for the neural operator framework.

Expert Commentary

The article makes a significant contribution to the field of control theory and machine learning. The proposed neural operator framework has the potential to revolutionize the way we approach multi-task control and adaptation problems. The authors' focus on generalization, efficiency, and adaptation is well-motivated, and the results demonstrate the effectiveness of the approach. However, as with any new framework, there are limitations and areas for further exploration. A more comprehensive comparative analysis and exploration of applications would strengthen the argument for the neural operator framework. Nevertheless, this article is a significant step forward in the field, and its implications are far-reaching.

Recommendations

  • ✓ Future research should investigate the application of neural operators in other areas, such as reinforcement learning or computer vision.
  • ✓ A more comprehensive comparison with existing methods, such as traditional reinforcement learning or meta-learning techniques, would strengthen the argument for the neural operator framework.

Sources

Original: arXiv - cs.LG

Related Articles