Active Learning for Estimating Reachable Sets for Systems With Unknown Dynamics.

Area of Science:

• Control Theory
• Machine Learning
• Computational Science

Background:

• Estimating reachable sets is crucial for system analysis but computationally intensive, especially for high-dimensional systems or when models are unavailable.
• Traditional set-based methods often struggle with scalability or require accurate system models.
• Generating data from black-box oracles is feasible but can be inefficient without intelligent sampling.

Purpose of the Study:

• To develop a data-driven method for computing reachable sets that overcomes the limitations of traditional approaches.
• To leverage active learning (AL) to reduce the computational burden associated with reachable set estimation.
• To apply the proposed framework to estimate domains of attraction for model predictive controllers (MPCs) and reinforcement learners.

Main Methods:

• Formulating reachable set estimation as a classification problem using generated state trajectory data.
• Employing active learning (AL) to intelligently select informative and dissimilar data samples.
• Utilizing submodularity for efficient selection of actively learned samples with bounded suboptimality.
• Introducing disagreement-based active learning (DBAL) to mitigate dependency on expensive oracles.

Main Results:

• Demonstrated efficient computation of reachable sets using AL for systems with unknown dynamics.
• Successfully estimated domains of attraction for MPCs and reinforcement learners.
• Showcased the effectiveness of DBAL in a solver selection problem for real-time MPC, reducing reliance on costly oracles.

Conclusions:

• Active learning provides a computationally efficient and scalable approach for reachable set estimation from data.
• The proposed DBAL framework enhances efficiency when dealing with multiple oracles with varying costs and accuracies.
• This data-driven methodology offers a practical solution for analyzing complex systems where traditional modeling is challenging.