Optimal Active Learning for Control-Oriented Identification of Nonlinear Dynamical Systems

Core Concepts

The core message of this work is to provide a finite sample analysis of an active learning algorithm for identifying nonlinear dynamical systems in a control-oriented manner, achieving optimal rates up to logarithmic factors.

Abstract

This paper introduces and analyzes the Active Learning for Control-Oriented Identification (ALCOI) algorithm, which extends previous work on active learning for model-based reinforcement learning to handle general nonlinear dynamical systems. The key contributions are: Finite sample analysis of ALCOI: The authors derive finite sample bounds on the excess control cost achieved by the ALCOI algorithm, which characterize the interplay between the hardness of control and the hardness of identification. These bounds are shown to be tight up to logarithmic factors in the setting of linear-in-the-parameters nonlinear systems. Novel non-asymptotic system identification result: The authors provide a new non-asymptotic result characterizing the parameter estimation error in terms of the Fisher Information matrix, which may be of independent interest. Two-stage exploration strategy: ALCOI uses a two-stage exploration strategy, where an initial coarse parameter estimate is first obtained, which is then used to design a targeted exploration policy that approximately solves an optimal experiment design problem. Numerical validation: The authors demonstrate the benefits of ALCOI over random exploration and approximate A-optimal experiment design on an illustrative nonlinear control problem. The key technical innovation is the use of recent advances in the non-asymptotic analysis of nonlinear system identification to derive end-to-end control guarantees for model-based reinforcement learning in general nonlinear settings.

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Active Learning for Control-Oriented Identification of Nonlinear Systems

by Bruce D. Lee... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.09030.pdf

Deeper Inquiries

How can the dependence of the burn-in time on the various system parameters be improved

To improve the dependence of the burn-in time on various system parameters, one could explore leveraging stability or reachability properties of the system. By incorporating these aspects into the algorithm, it may be possible to optimize the burn-in time more effectively. Additionally, considering the specific characteristics of the system dynamics and the control objectives could help tailor the burn-in time to the specific requirements of the problem. By customizing the burn-in time based on the system's unique features, the algorithm can be further optimized for efficiency and effectiveness.

Can the authors' approach be extended to handle partially observed dynamics or other more general settings

The authors' approach could potentially be extended to handle partially observed dynamics or other more general settings by incorporating techniques from prediction error methods. These methods are designed to handle situations where only partial information about the system dynamics is available. By integrating prediction error methods into the ALCOI algorithm, it may be possible to address scenarios with incomplete observations or more complex system dynamics. This extension could enhance the algorithm's applicability to a wider range of real-world problems where full observability is not feasible.

What are the computational considerations for implementing the ALCOI algorithm in practice, and how can the efficiency be further improved

In practice, implementing the ALCOI algorithm may involve computational considerations related to data collection, system identification, and control synthesis. To enhance efficiency, optimizing the algorithm's data collection strategy, such as selecting informative experiments and minimizing redundant data, can help reduce computational complexity. Additionally, leveraging parallel computing or distributed systems can expedite the processing of large datasets and computations involved in system identification and control synthesis. Furthermore, optimizing the algorithm's implementation by utilizing efficient data structures and algorithms can enhance its computational performance. Continuous refinement and optimization of the algorithm's implementation can further improve its efficiency in practice.