Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions

TL;DR

This paper introduces a provably sample-efficient safe learning framework for nonlinear control that combines control barrier functions with optimistic exploration, ensuring safety and near-optimal performance during online learning.

Contribution

It extends control barrier functions to stochastic settings and integrates an exploration strategy for safe, efficient learning in unknown nonlinear systems.

Findings

Achieves high-probability safety guarantees under uncertainty.

Provides regret bounds against the optimal controller.

Demonstrates effectiveness through simulation results.

Abstract

Reinforcement Learning (RL) and continuous nonlinear control have been successfully deployed in multiple domains of complicated sequential decision-making tasks. However, given the exploration nature of the learning process and the presence of model uncertainty, it is challenging to apply them to safety-critical control tasks due to the lack of safety guarantee. On the other hand, while combining control-theoretical approaches with learning algorithms has shown promise in safe RL applications, the sample efficiency of safe data collection process for control is not well addressed. In this paper, we propose a \emph{provably} sample efficient episodic safe learning framework for online control tasks that leverages safe exploration and exploitation in an unknown, nonlinear dynamical system. In particular, the framework 1) extends control barrier functions (CBFs) in a stochastic setting to achieve provable high-probability safety under uncertainty during model learning and 2) integrates an optimism-based exploration strategy to efficiently guide the safe exploration process with learned dynamics for \emph{near optimal} control performance. We provide formal analysis on the episodic regret bound against the optimal controller and probabilistic safety with theoretical guarantees. Simulation results are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.