We consider the problem of learning a Constrained Markov Decision Process (CMDP) via general parameterization. Our proposed Primal-Dual based Regularized Accelerated Natural Policy Gradient (PDR-ANPG) algorithm uses entropy and quadratic regularizers to reach this goal. For a parameterized policy class with transferred compatibility approximation error, $\epsilon_{\mathrm{bias}}$, PDR-ANPG achieves a last-iterate $\epsilon$ optimality gap and $\epsilon$ constraint violation (up to some additive factor of $\epsilon_{\mathrm{bias}}$) with a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-2}\min\{\epsilon^{-2},\epsilon_{\mathrm{bias}}^{-\frac{1}{3}}\})$. If the class is incomplete ($\epsilon_{\mathrm{bias}}>0$), then the sample complexity reduces to $\tilde{\mathcal{O}}(\epsilon^{-2})$ for $\epsilon<(\epsilon_{\mathrm{bias}})^{\frac{1}{6}}$. Moreover, for complete policies with $\epsilon_{\mathrm{bias}}=0$, our algorithm achieves a last-iterate $\epsilon$ optimality gap and $\epsilon$ constraint violation with $\tilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity. It is a significant improvement of the state-of-the-art last-iterate guarantees of general parameterized CMDPs.

本研究旨在解决学习受限马尔可夫决策过程（CMDP）中的一般参数化问题，并提出了一种基于原始-对偶的正则化加速自然策略梯度（PDR-ANPG）算法。该算法在样本复杂度方面显著提升了当前CMDP的一般参数化策略的最后迭代保障，展示了具有潜在影响的高效收敛性。

受限马尔可夫决策过程中的一般参数化策略的最后迭代收敛性