# Closing the Gap: Achieving Global Convergence (Last Iterate) of Actor-Critic under Markovian Sampling with Neural Network Parametrization

arXiv: https://arxiv.org/abs/2405.01843 · HTML: https://mlsanity.com/paper/2405.01843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- First posted on arXiv 3 May 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Built on by (most cited first, 1 of 1)

- [Schrödinger--Föllmer Actor--Critic: Diffusion Policy Improvement with Finite-Sample Analysis](https://mlsanity.com/paper/2609.33239/) (2026)

## Abstract (arXiv)

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: Multi-layer neural network parametrization for actor/critic, Markovian sampling, Continuous state-action spaces, the performance of the Last iterate, and Global 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 tildeOleft(ε-3right). 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.