Summary of Regret Bounds For Episodic Risk-sensitive Linear Quadratic Regulator, by Wenhao Xu et al.
Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator
by Wenhao Xu, Xuefeng Gao, Xuedong He
First submitted to arxiv on: 8 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes novel algorithms for online adaptive control of risk-sensitive linear quadratic regulators in finite-horizon episodic settings. The least-squares greedy algorithm achieves logarithmic regret under specific identifiability assumptions, while incorporating exploration noise yields a algorithm with square-root regret bounds when these conditions are not met. This work establishes the first regret bounds for episodic risk-sensitive linear quadratic regulators and relies on perturbation analysis of Riccati equations and loss analysis in the risk-sensitive performance criterion. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Risk-sensitive linear quadratic regulator is an important problem in control theory, and this paper develops new methods to solve it online. The algorithms use least-squares and exploration noise to balance exploration and exploitation. The results show that these methods can achieve good performance with a logarithmic or square-root regret bound. This is the first time anyone has proven bounds for risk-sensitive linear quadratic regulator in episodic settings. |
