Direct Latent Model Learning for Linear Quadratic Gaussian Control

Concepts de base

Direct latent model learning with cost-driven state representation can solve Linear Quadratic Gaussian (LQG) control problems efficiently.

Résumé

The study focuses on learning state representations for controlling partially observable systems using a direct latent model approach. It emphasizes the importance of predicting multi-step costs and avoiding observation reconstruction. The method aims to find near-optimal state representation functions and controllers through finite-sample guarantees. By parameterizing the state representation function and identifying latent system dynamics, the approach offers a viable solution for LQG control.

Stats

Prior to this work, it was unclear if cost-driven latent model learners had finite-sample guarantees.
The quadratic regression problem arises due to the inherent quadratic form of the cost function in LQG.
The controllability matrix ensures that there are control inputs to drive the state to zero in a certain number of steps.

Citations

"Our work underscores the value of predicting multi-step costs, an idea that is key to our theory."
"Cost-driven state representation learning is more direct than observation-reconstruction-based methods."
"The method provides a viable path to solving LQG control problems."

Idées clés tirées de

Can Direct Latent Model Learning Solve Linear Quadratic Gaussian Control?

by Yi Tian,Kaiq... à arxiv.org 03-14-2024

https://arxiv.org/pdf/2212.14511.pdf

Questions plus approfondies

How does the approach compare to traditional observation-reconstruction-based methods

The approach of cost-driven state representation learning presented in the context differs from traditional observation-reconstruction-based methods in several key aspects.
Observation-reconstruction-based methods typically involve learning a mapping from observed data to latent states by reconstructing observations using an autoencoder or similar techniques. This process requires predicting observations and then using them as supervision for representation learning. In contrast, the cost-driven approach focuses on directly predicting multi-step cumulative costs related to planning without reconstructing observations. By bypassing the reconstruction step, the cost-driven method aims to learn state representations that are directly relevant for control purposes.
Furthermore, while observation-reconstruction-based methods may recover all state components based on reconstructed observations, the cost-driven approach targets recovering only the state components relevant to costs. This targeted approach can lead to more efficient and effective state representations specifically tailored for control tasks.
In summary, the cost-driven state representation learning method offers a more direct and focused way of learning state representations compared to traditional observation-reconstruction-based methods.

What are the implications of not having full-rank covariances in the learned latent states

Not having full-rank covariances in learned latent states can have significant implications for system identification and controller design. When latent states do not have full-rank covariances, it means that certain dimensions of these states are not fully captured or utilized in representing the underlying system dynamics.
In practical terms, this limitation can result in incomplete information about the system's behavior being encoded into the learned latent states. As a consequence, controllers designed based on these incomplete representations may not fully exploit all available information for optimal control performance.
To address this issue effectively, it is crucial to ensure that latent states have full-rank covariances through appropriate training strategies or modifications to the learning algorithm. By ensuring full-rank covariances in learned latent states, we can enhance system identifiability and improve controller design accuracy.

How can these findings be applied to other types of control systems beyond LQG

The findings from this study on LQG control systems can be applied beyond this specific domain to other types of control systems with partially observable dynamics. Here are some ways these findings could be extended:

Nonlinear Systems: The principles of cost-driven state representation learning could be adapted for nonlinear systems where traditional observability concepts may not apply directly.

Reinforcement Learning: The concept of predicting multi-step cumulative costs as a supervision signal could be integrated into reinforcement learning algorithms across various domains.

Real-world Applications: Applying these findings to real-world scenarios such as robotics (e.g., robotic manipulation) or autonomous vehicles (e.g., self-driving cars) could lead to improved control strategies based on more accurate and efficient state representations.

By generalizing these insights beyond LQG systems, researchers and practitioners can explore new avenues for enhancing control methodologies across diverse applications requiring intelligent decision-making processes based on partial observations.