Saved in:
Bibliographic Details
Main Authors: Tian, Yi, Zhang, Kaiqing, Tedrake, Russ, Sra, Suvrit
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2212.14511
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914376551759872
author Tian, Yi
Zhang, Kaiqing
Tedrake, Russ
Sra, Suvrit
author_facet Tian, Yi
Zhang, Kaiqing
Tedrake, Russ
Sra, Suvrit
contents We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a cost-driven approach, where a dynamic model in some latent state space is learned by predicting the costs without predicting the observations or actions. In particular, we focus on an intuitive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems. As our main results, we establish finite-sample guarantees of finding a near-optimal state representation function and a near-optimal controller using the directly learned latent model, for finite-horizon time-varying LQG control problems. To the best of our knowledge, despite various empirical successes, finite-sample guarantees of such a cost-driven approach remain elusive. Our result underscores the value of predicting multi-step costs, an idea that is key to our theory, and notably also an idea that is known to be empirically valuable for learning state representations. A second part of this work, that is to appear as Part II, addresses the infinite-horizon linear time-invariant setting; it also extends the results to an approach that implicitly learns the latent dynamics, inspired by the recent empirical breakthrough of MuZero in model-based reinforcement learning.
format Preprint
id arxiv_https___arxiv_org_abs_2212_14511
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I
Tian, Yi
Zhang, Kaiqing
Tedrake, Russ
Sra, Suvrit
Machine Learning
Systems and Control
Optimization and Control
We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a cost-driven approach, where a dynamic model in some latent state space is learned by predicting the costs without predicting the observations or actions. In particular, we focus on an intuitive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems. As our main results, we establish finite-sample guarantees of finding a near-optimal state representation function and a near-optimal controller using the directly learned latent model, for finite-horizon time-varying LQG control problems. To the best of our knowledge, despite various empirical successes, finite-sample guarantees of such a cost-driven approach remain elusive. Our result underscores the value of predicting multi-step costs, an idea that is key to our theory, and notably also an idea that is known to be empirically valuable for learning state representations. A second part of this work, that is to appear as Part II, addresses the infinite-horizon linear time-invariant setting; it also extends the results to an approach that implicitly learns the latent dynamics, inspired by the recent empirical breakthrough of MuZero in model-based reinforcement learning.
title Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I
topic Machine Learning
Systems and Control
Optimization and Control
url https://arxiv.org/abs/2212.14511