# Global Convergence of Average Reward Constrained MDPs with Neural Critic and General Policy Parameterization

arXiv: https://arxiv.org/abs/2603.07698 · HTML: https://mlsanity.com/paper/2603.07698/

## 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.
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee](https://mlsanity.com/paper/2011.05869/) (2020)
- [Stochastic Variance-Reduced Policy Gradient](https://mlsanity.com/paper/1806.05618/) (2018)
- [On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method](https://mlsanity.com/paper/2102.08607/) (2021)
- [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)
- [DeepPool: Distributed Model-free Algorithm for Ride-sharing using Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03882/) (2019)
- [Single-Timescale Actor-Critic Provably Finds Globally Optimal Policy](https://mlsanity.com/paper/2008.00483/) (2020)
- [Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints](https://mlsanity.com/paper/2202.00150/) (2022)
- [Finite-Sample Analysis of Off-Policy Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2102.09318/) (2021)
- [Improved Sample Complexity Analysis of Natural Policy Gradient Algorithm with General Parameterization for Infinite Horizon Discounted Reward Markov Decision Processes](https://mlsanity.com/paper/2310.11677/) (2023)
- [Finite-Time Analysis of Entropy-Regularized Neural Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2206.00833/) (2022)
- [Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Conservative Natural Policy Gradient Primal-Dual Algorithm](https://mlsanity.com/paper/2206.05850/) (2022)
- [Concave Utility Reinforcement Learning with Zero-Constraint Violations](https://mlsanity.com/paper/2109.05439/) (2021)
- [First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities](https://mlsanity.com/paper/2305.15938/) (2023)
- [Sample-Efficient Constrained Reinforcement Learning with General Parameterization](https://mlsanity.com/paper/2405.10624/) (2024)
- [Learning General Parameterized Policies for Infinite Horizon Average Reward Constrained MDPs via Primal-Dual Policy Gradient Algorithm](https://mlsanity.com/paper/2402.02042/) (2024)
- [Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm](https://mlsanity.com/paper/2505.15138/) (2025)
- [Regret Analysis of Average-Reward Unichain MDPs via an Actor-Critic Approach](https://mlsanity.com/paper/2505.19986/) (2025)
- [Reinforced Sequential Decision-Making for Sepsis Treatment: The POSNEGDM Framework with Mortality Classifier and Transformer](https://mlsanity.com/paper/2403.07309/) (2024)
- [An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks](https://mlsanity.com/paper/2405.04017/) (2024)
- [Regret Analysis of Unichain Average Reward Constrained MDPs with General Parameterization](https://mlsanity.com/paper/2602.08000/) (2026)

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

- [Learning Weakly Communicating Average-Reward CMDPs: Strong Duality and Improved Regret](https://mlsanity.com/paper/2605.11586/) (2026)

## Abstract (arXiv)

We study infinite-horizon Constrained Markov Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on tabular policies or linear critics, which limits their applicability to high-dimensional and continuous control problems. We propose a primal-dual natural actor-critic algorithm that integrates neural critic estimation with natural policy gradient updates and leverages Neural Tangent Kernel (NTK) theory to control function-approximation error under Markovian sampling, without requiring access to mixing-time oracles. We establish global convergence and cumulative constraint violation rates of tildeO(T^-1/4) up to approximation errors induced by the policy and critic classes. Our results provide the first such guarantees for CMDPs with general policies and multi-layer neural critics, substantially extending the theoretical foundations of actor-critic methods beyond the linear-critic regime.