# Neural Policy Gradient Methods: Global Optimality and Rates of Convergence

arXiv: https://arxiv.org/abs/1909.01150 · HTML: https://mlsanity.com/paper/1909.01150/

## Key facts

- Cited by 159 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2019.

## Built on by (most cited first, 30 of 159)

- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [Jump-Start Reinforcement Learning](https://mlsanity.com/paper/2204.02372/) (2022)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Online Robust Reinforcement Learning with Model Uncertainty](https://mlsanity.com/paper/2109.14523/) (2021)
- [Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence](https://mlsanity.com/paper/2105.11066/) (2021)
- [A general sample complexity analysis of vanilla policy gradient](https://mlsanity.com/paper/2107.11433/) (2021)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods](https://mlsanity.com/paper/2211.07937/) (2022)
- [Stochastic Policy Gradient Methods: Improved Sample Complexity for Fisher-non-degenerate Policies](https://mlsanity.com/paper/2302.01734/) (2023)
- [Softmax Policy Gradient Methods Can Take Exponential Time to Converge](https://mlsanity.com/paper/2102.11270/) (2021)
- [On the Linear convergence of Natural Policy Gradient Algorithm](https://mlsanity.com/paper/2105.01424/) (2021)
- [Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies](https://mlsanity.com/paper/2210.01400/) (2022)
- [Towards General Function Approximation in Zero-Sum Markov Games](https://mlsanity.com/paper/2107.14702/) (2021)
- [Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization](https://mlsanity.com/paper/2401.15604/) (2024)
- [Finite Sample Analysis of Two-Time-Scale Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2101.10506/) (2021)
- [On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)](https://mlsanity.com/paper/2109.04024/) (2021)
- [Finite-time analysis of single-timescale actor-critic](https://mlsanity.com/paper/2210.09921/) (2022)
- [Policy Optimization for Continuous Reinforcement Learning](https://mlsanity.com/paper/2305.18901/) (2023)
- [A Novel Framework for Policy Mirror Descent with General Parameterization and Linear Convergence](https://mlsanity.com/paper/2301.13139/) (2023)
- [Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian](https://mlsanity.com/paper/2211.00716/) (2022)
- [Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approach](https://mlsanity.com/paper/2108.02731/) (2021)
- [Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs](https://mlsanity.com/paper/2306.11700/) (2023)
- [Convergence and sample complexity of natural policy gradient primal-dual methods for constrained MDPs](https://mlsanity.com/paper/2206.02346/) (2022)
- [Finite-Sample Analysis of Off-Policy Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2102.09318/) (2021)
- [Sample and Communication-Efficient Decentralized Actor-Critic Algorithms with Finite-Time Analysis](https://mlsanity.com/paper/2109.03699/) (2021)
- [On the Global Optimum Convergence of Momentum-based Policy Gradient](https://mlsanity.com/paper/2110.10116/) (2021)
- [Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes](https://mlsanity.com/paper/2309.01922/) (2023)

## Abstract (arXiv)

Policy gradient methods with actor-critic schemes demonstrate tremendous empirical successes, especially when the actors and critics are parameterized by neural networks. However, it remains less clear whether such "neural" policy gradient methods converge to globally optimal policies and whether they even converge at all. We answer both the questions affirmatively in the overparameterized regime. In detail, we prove that neural natural policy gradient converges to a globally optimal policy at a sublinear rate. Also, we show that neural vanilla policy gradient converges sublinearly to a stationary point. Meanwhile, by relating the suboptimality of the stationary points to the representation power of neural actor and critic classes, we prove the global optimality of all stationary points under mild regularity conditions. Particularly, we show that a key to the global optimality and convergence is the "compatibility" between the actor and critic, which is ensured by sharing neural architectures and random initializations across the actor and critic. To the best of our knowledge, our analysis establishes the first global optimality and convergence guarantees for neural policy gradient methods.