Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning

Abstract

In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their key components that adapt to underlying structures of the problem. Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret bounds for two model-free algorithms under episodic Markov decision processes. We show that, in appropriate settings, these bounds feature exponential improvement over existing ones that are independent of gaps. We also prove gap-dependent lower bounds, which certify the near optimality of the upper bounds.

Cite

Text

Fei and Xu. "Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning." International Conference on Machine Learning, 2022.

Markdown

[Fei and Xu. "Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning." International Conference on Machine Learning, 2022.](https://mlanthology.org/icml/2022/fei2022icml-cascaded/)

BibTeX

@inproceedings{fei2022icml-cascaded,
  title     = {{Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning}},
  author    = {Fei, Yingjie and Xu, Ruitu},
  booktitle = {International Conference on Machine Learning},
  year      = {2022},
  pages     = {6392-6417},
  volume    = {162},
  url       = {https://mlanthology.org/icml/2022/fei2022icml-cascaded/}
}