Offline Supervised Learning and Online Direct Policy Optimization for Efficient Neural Network-Based Optimal Feedback Control

Core Concepts

Offline supervised learning and online direct policy optimization are two prevalent approaches for training neural network-based optimal feedback controllers. Offline supervised learning leverages pre-computed open-loop optimal control solutions, while online direct policy optimization transforms the optimal control problem into a direct optimization problem. This work conducts a comparative study of the two approaches and proposes a unified training paradigm, Pre-Train and Fine-Tune, that combines their strengths to significantly enhance performance and robustness.

Abstract

The content presents a comparative study of two prevalent approaches for training neural network-based optimal feedback controllers: offline supervised learning and online direct policy optimization.
Offline Supervised Learning:

Trains a feedback network controller by approximating the corresponding open-loop solutions at different states.
The learning signal comes from the open-loop optimal control solution, which is much easier to solve than the closed-loop control.
The key challenge is generating a high-quality dataset using open-loop optimal control solvers.
Online Direct Policy Optimization:

Transforms the network-based feedback optimal control problem into an optimization problem and solves it directly without pre-computing open-loop optimal control.
The objective function comes directly from the original optimal control problem.
The main challenge is the optimization process, as the dynamics-related objective can be hard to optimize when the problem is complicated.
The comparative analysis shows that offline supervised learning holds advantages over direct policy optimization in terms of optimality and training time. However, direct policy optimization can yield further performance enhancements with a near-optimally initialized network.
To overcome the limitations of the two approaches, the authors propose a unified training paradigm, Pre-Train and Fine-Tune. It first pre-trains the network through offline supervised learning to guide it to a reasonable solution, then fine-tunes it through online direct policy optimization to break the limitations of the precomputed dataset and further improve the controller's performance and robustness.
Experiments on optimal attitude control of a satellite and optimal landing of a quadrotor demonstrate the superiority of the Pre-Train and Fine-Tune strategy over the individual approaches.

Stats

The average time to solve an open-loop solution for one trajectory in the satellite problem is about 0.5 seconds.
It takes less than 1 minute to generate the whole optimal control dataset for the satellite problem without parallel computing.
It costs more than 1 hour to train 2000 iterations of direct policy optimization from scratch for the satellite problem.

Quotes

"Offline supervised learning is to train a feedback network controller by approximating the corresponding open-loop solutions at different states directly, leveraging the fact that open-loop control for a fixed initial state is much easier to solve than feedback control in optimal control problems (OCP)."
"The other way, online direct policy optimization, transforms the network-based feedback OCP concerning a distribution of initial states into an optimization problem and solves it directly without pre-computing open-loop optimal control."
"Our results underscore the superiority of offline supervised learning in terms of both optimality and training time."

Key Insights Distilled From

Offline Supervised Learning V.S. Online Direct Policy Optimization

by Yue Zhao,Jie... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2211.15930.pdf

Deeper Inquiries

How can the proposed Pre-Train and Fine-Tune strategy be extended to handle more complex optimal control problems with uncertain or partially known dynamics?

The Pre-Train and Fine-Tune strategy can be extended to handle more complex optimal control problems with uncertain or partially known dynamics by incorporating techniques to address the uncertainty in the system dynamics. One approach is to introduce robust optimization methods that can account for uncertainties in the system parameters or disturbances. This can involve adding robustness constraints to the optimization problem or using robust control techniques to ensure stability and performance under uncertain conditions.
Another way to handle uncertain dynamics is to incorporate model predictive control (MPC) into the training paradigm. MPC is well-suited for systems with uncertain dynamics as it uses a model of the system to predict future behavior and optimize control actions over a finite time horizon. By integrating MPC into the Pre-Train and Fine-Tune strategy, the neural network controller can adapt to changing dynamics and disturbances in real-time.
Furthermore, the strategy can be extended to handle more complex problems by incorporating advanced machine learning techniques such as Bayesian optimization or reinforcement learning. Bayesian optimization can be used to optimize hyperparameters and model uncertainties, while reinforcement learning can enable the controller to learn from interactions with the environment and adapt to unknown dynamics over time.

What are the potential limitations of the unified training paradigm, and how can it be further improved to handle a wider range of optimal control applications?

One potential limitation of the unified training paradigm is the reliance on pre-training through supervised learning, which may not always capture the full complexity of the optimal control problem. To address this limitation, the strategy can be further improved by incorporating more advanced optimization algorithms that can handle high-dimensional and non-linear systems more effectively. Additionally, the dataset generation process can be enhanced by using more sophisticated numerical methods or adaptive sampling techniques to ensure a more diverse and representative dataset.
Another limitation is the assumption of fully-known dynamics, which may not hold in real-world applications. To improve the strategy's applicability to a wider range of optimal control applications, methods for handling uncertain or partially known dynamics should be integrated. This could involve incorporating uncertainty quantification techniques, such as probabilistic modeling or ensemble methods, to account for model inaccuracies and disturbances in the system.
Furthermore, the unified training paradigm can be enhanced by incorporating domain knowledge and expert insights into the training process. By leveraging domain-specific information, the controller can be tailored to the specific characteristics of the optimal control problem, leading to improved performance and robustness.

What insights can be gained from this study to inform the development of more efficient and robust reinforcement learning algorithms for solving high-dimensional optimal control problems?

This study provides valuable insights into the comparative analysis of different training approaches for neural network-based optimal control problems. These insights can inform the development of more efficient and robust reinforcement learning algorithms for solving high-dimensional optimal control problems in the following ways:

Hybrid Approaches: By combining the strengths of offline supervised learning and online direct policy optimization, hybrid reinforcement learning algorithms can be developed to leverage the benefits of both approaches. This can lead to improved performance and robustness in solving high-dimensional optimal control problems.

Adaptive Sampling: Insights from the study highlight the importance of dataset quality in training neural network controllers. Reinforcement learning algorithms can benefit from adaptive sampling techniques to generate high-quality datasets that capture the complexity of the optimal control problem more effectively.

Robust Optimization: The study underscores the challenges of optimization in direct policy optimization. Robust optimization techniques can be integrated into reinforcement learning algorithms to ensure stability and performance under uncertain conditions, making them more suitable for high-dimensional optimal control problems.

By incorporating these insights into the development of reinforcement learning algorithms, researchers can create more efficient and robust solutions for solving complex optimal control problems in various domains.