We study the regret guarantee for risk-sensitive reinforcement learning (RSRL) via distributional reinforcement learning (DRL) methods. In particular, we consider finite episodic Markov decision processes whose objective is the entropic risk measure (EntRM) of return. We identify a key property of the EntRM, the monotonicity-preserving property, which enables the risk-sensitive distributional dynamic programming framework. We then propose two novel DRL algorithms that implement optimism through two different schemes, including a model-free one and a model-based one. We prove that both of them attain $\tilde{\mathcal{O}}(\frac{\exp(|\beta| H)-1}{|\beta|H}H\sqrt{HS^2AT})$ regret upper bound, where $S$ is the number of states, $A$ the number of states, $H$ the time horizon and $T$ the number of total time steps. It matches RSVI2 proposed in \cite{fei2021exponential} with a much simpler regret analysis. To the best of our knowledge, this is the first regret analysis of DRL, which bridges DRL and RSRL in terms of sample complexity. Finally, we improve the existing lower bound by proving a tighter bound of $\Omega(\frac{\exp(\beta H/6)-1}{\beta H}H\sqrt{SAT})$ for $\beta>0$ case, which recovers the tight lower bound $\Omega(H\sqrt{SAT})$ in the risk-neutral setting.

研究了通过分布式强化学习方法实现风险敏感强化学习的后悔保证，提出了两种新的DRL算法，并通过样本复杂度桥接了DRL和RSRL。同时还改进了现有的下限，并提出了更紧的下限。

通过可证明遗憾界实现分布式和风险敏感的强化学习