The current state-of-the-art theoretical analysis of Actor-Critic (AC) algorithms significantly lags in addressing the practical aspects of AC implementations. This crucial gap needs bridging to bring the analysis in line with practical implementations of AC. To address this, we advocate for considering the MMCLG criteria: \textbf{M}ulti-layer neural network parametrization for actor/critic, \textbf{M}arkovian sampling, \textbf{C}ontinuous state-action spaces, the performance of the \textbf{L}ast iterate, and \textbf{G}lobal optimality. These aspects are practically significant and have been largely overlooked in existing theoretical analyses of AC algorithms. In this work, we address these gaps by providing the first comprehensive theoretical analysis of AC algorithms that encompasses all five crucial practical aspects (covers MMCLG criteria). We establish global convergence sample complexity bounds of $\tilde{\mathcal{O}}\left({\epsilon^{-3}}\right)$. We achieve this result through our novel use of the weak gradient domination property of MDP's and our unique analysis of the error in critic estimation.

翻译：当前演员-评论家（AC）算法的理论分析在解决实际实现方面显著滞后。这一关键差距亟待弥合，以使分析接近AC的实际应用。为此，我们主张考虑MMCLG准则：演员/评论家的\textbf{多}层神经网络参数化、\textbf{马}尔可夫采样、\textbf{连}续状态-动作空间、\textbf{末}次迭代性能以及\textbf{全}局最优性。这些方面具有实际重要性，但在现有的AC算法理论分析中很大程度上被忽视。本文通过首次涵盖所有五个关键实际方面（即满足MMCLG准则）的综合理论分析来填补这些空白。我们建立了全局收敛的样本复杂度界$\tilde{\mathcal{O}}\left({\epsilon^{-3}}\right)$。通过创新性地利用马尔可夫决策过程（MDP）的弱梯度主导性质以及对评论家估计误差的独特分析，我们取得了这一结果。