Closed-loop Model Selection for Kernel-based Models using Bayesian Optimization

TL;DR

This paper introduces a Bayesian optimization framework to select kernels and hyperparameters for kernel-based models specifically tailored to improve closed-loop control performance in nonlinear systems, demonstrated on simulations and a robotic arm.

Contribution

It presents a novel method to optimize kernel hyperparameters directly for control performance, bridging the gap between model accuracy and control effectiveness.

Findings

Improved control performance through optimized kernel selection.

Effective application demonstrated on a robotic arm.

Framework converges to desired control performance.

Abstract

Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian optimization to iteratively refine the kernel-based model using the observed performance on the actual system until a desired performance is achieved. We demonstrate the proposed approach in a simulation and on a 3-DoF robotic arm.