Risk-averse reinforcement learning (RARL) is critical for decision-making under uncertainty, which is especially valuable in high-stake applications. However, most existing works focus on risk measures, e.g., conditional value-at-risk (CVaR), while measures of variability remain underexplored. In this paper, we comprehensively study nine common measures of variability, namely Variance, Gini Deviation, Mean Deviation, Mean-Median Deviation, Standard Deviation, Inter-Quantile Range, CVaR Deviation, Semi_Variance, and Semi_Standard Deviation. Among them, four metrics have not been previously studied in RARL. We derive policy gradient formulas for these unstudied metrics, improve gradient estimation for Gini Deviation, analyze their gradient properties, and incorporate them with the REINFORCE and PPO frameworks to penalize the dispersion of returns. Our empirical study reveals that variance-based metrics lead to unstable policy updates. In contrast, CVaR Deviation and Gini Deviation show consistent performance across different randomness and evaluation domains, achieving high returns while effectively learning risk-averse policies. Mean Deviation and Semi_Standard Deviation are also competitive across different scenarios. This work provides a comprehensive overview of variability measures in RARL, offering practical insights for risk-aware decision-making and guiding future research on risk metrics and RARL algorithms.

本研究针对现有风险规避强化学习(RARL)文献中对变异性度量研究不足的问题，系统地分析了九种常见的变异性度量方法，并提出了针对未研究度量的策略梯度公式。研究发现，CVaR Deviation 和 Gini Deviation 在多种随机性及评估领域表现出一致的性能，为风险规避决策提供了重要的实用见解及未来研究的方向。

风险规避策略梯度的变异性度量