Closing the Gap: Achieving Global Convergence (Last Iterate) of Actor-Critic under Markovian Sampling with Neural Network Parametrization
Abstract
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 . 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.
Keywords
Cite
@article{arxiv.2405.01843,
title = {Closing the Gap: Achieving Global Convergence (Last Iterate) of Actor-Critic under Markovian Sampling with Neural Network Parametrization},
author = {Mudit Gaur and Amrit Singh Bedi and Di Wang and Vaneet Aggarwal},
journal= {arXiv preprint arXiv:2405.01843},
year = {2024}
}
Comments
Accepted at ICML 2024. This is a revised version of arXiv:2306.10486, where we have gone from finite action space to continuous action space, from average iterate convergence to last iterate convergence and from $\epsilon^{-4}$ to $\epsilon^{-3}$ sample complexity. This version fixes the related work result of (Xu et al., 2020a), based on their result update on arXiv