Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation.

Area of Science:

• Control Theory
• Machine Learning
• Optimization

Background:

• Reinforcement learning (RL) often struggles with safety guarantees, especially in uncertain systems.
• Approximate dynamic programming (ADP) offers a framework for sequential decision-making under uncertainty.
• Ensuring stability and constraint satisfaction is crucial for real-world RL applications.

Purpose of the Study:

• To develop a method for generating safe initial policies in reinforcement learning for discrete-time uncertain systems.
• To provide provable guarantees for the safety and stability of learned control policies.
• To enable constraint enforcement during the initial phases of policy learning.

Main Methods:

• Utilized approximate dynamic programming (ADP) techniques for policy development.
• Employed kernelized Lipschitz estimation to learn crucial multiplier matrices.
• Leveraged semidefinite programming (SDP) frameworks to compute admissible initial control policies.

Main Results:

• Successfully computed admissible initial control policies with provably high probability.
• Demonstrated that these admissible controllers ensure safe initialization and constraint enforcement.
• Showcased the ability of the method to provide exponential stability for the closed-loop system's equilibrium.

Conclusions:

• The proposed method effectively addresses the challenge of safe policy initialization in RL for uncertain systems.
• Kernelized Lipschitz estimation and SDP provide a robust framework for guaranteeing policy safety and system stability.
• This work advances the practical applicability of RL in safety-critical domains.