We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary arbitrarily over time with a budget on their cumulative variations. When this variation budget is known a prior, we propose two restart-based algorithms, namely Restart-RSMB and Restart-RSQ, and establish their dynamic regrets. Based on these results, we further present a meta-algorithm that does not require any prior knowledge of the variation budget and can adaptively detect the non-stationarity on the exponential value functions. A dynamic regret lower bound is then established for non-stationary risk-sensitive RL to certify the near-optimality of the proposed algorithms. Our results also show that the risk control and the handling of the non-stationarity can be separately designed in the algorithm if the variation budget is known a prior, while the non-stationary detection mechanism in the adaptive algorithm depends on the risk parameter. This work offers the first non-asymptotic theoretical analyses for the non-stationary risk-sensitive RL in the literature.

研究使用熵风险度量在非平稳有限马尔可夫决策过程中采用风险敏感强化学习，提出了两种基于重启的算法以及自适应检测不稳定性的元算法，并证明了算法的动态后悔下界。该研究为文献中的非平稳风险敏感强化学习提供了首个非渐近理论分析。

非平稳风险敏感强化学习: 近似最优动态遗憾、自适应检测和分离设计