# Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator

arXiv: https://arxiv.org/abs/2406.05366 · HTML: https://mlsanity.com/paper/2406.05366/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problems](https://mlsanity.com/paper/2407.17226/) (2024)

## Abstract (arXiv)

Risk-sensitive linear quadratic regulator is one of the most fundamental problems in risk-sensitive optimal control. In this paper, we study online adaptive control of risk-sensitive linear quadratic regulator in the finite horizon episodic setting. We propose a simple least-squares greedy algorithm and show that it achieves widetildeO(log N) regret under a specific identifiability assumption, where N is the total number of episodes. If the identifiability assumption is not satisfied, we propose incorporating exploration noise into the least-squares-based algorithm, resulting in an algorithm with widetildeO(√N) regret. To our best knowledge, this is the first set of regret bounds for episodic risk-sensitive linear quadratic regulator. Our proof relies on perturbation analysis of less-standard Riccati equations for risk-sensitive linear quadratic control, and a delicate analysis of the loss in the risk-sensitive performance criterion due to applying the suboptimal controller in the online learning process.