On the Effect of Quadratic Regularization in Direct Data-Driven LQR

TL;DR

This paper introduces an explainability framework for data-driven LQR with quadratic regularization, clarifying how regularization influences system parameters and reducing computational complexity.

Contribution

It presents a novel analysis approach that interprets regularization effects and eliminates auxiliary variables in data-driven LQR, enhancing understanding and efficiency.

Findings

Regularization effects can be interpreted through system quantities.

The proposed method reduces computational complexity.

Simulations demonstrate the effectiveness of the approach.

Abstract

This paper proposes an explainability concept for direct data-driven linear quadratic regulation (LQR) with quadratic regularization. Our perspective follows the parametric effect of regularization, an analysis approach that translates regularization costs from auxiliary variables to system quantities, enabling intuitive interpretations. The framework further enables the elimination of auxiliary variables, thereby reducing computational complexity. We demonstrate the effectiveness of our approach and the identified effect of regularization via simulations.