# Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes

arXiv: https://arxiv.org/abs/2309.01922 · HTML: https://mlsanity.com/paper/2309.01922/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes](https://mlsanity.com/paper/1910.07072/) (2019)
- [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)
- [Efficient Bias-Span-Constrained Exploration-Exploitation in Reinforcement Learning](https://mlsanity.com/paper/1802.04020/) (2018)
- [Learning Unknown Markov Decision Processes: A Thompson Sampling Approach](https://mlsanity.com/paper/1709.04570/) (2017)
- [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)
- [Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation](https://mlsanity.com/paper/2007.11849/) (2020)
- [Adapting to Mixing Time in Stochastic Optimization with Markovian Data](https://mlsanity.com/paper/2202.04428/) (2022)
- [Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints](https://mlsanity.com/paper/2202.00150/) (2022)
- [Deep Reinforcement Learning Based Intelligent Reflecting Surface for Secure Wireless Communications](https://mlsanity.com/paper/2002.12271/) (2020)
- [Concave Utility Reinforcement Learning with Zero-Constraint Violations](https://mlsanity.com/paper/2109.05439/) (2021)
- [Beyond Exponentially Fast Mixing in Average-Reward Reinforcement Learning via Multi-Level Monte Carlo Actor-Critic](https://mlsanity.com/paper/2301.12083/) (2023)
- [Cooperating Graph Neural Networks with Deep Reinforcement Learning for Vaccine Prioritization](https://mlsanity.com/paper/2305.05163/) (2023)

## Built on by (most cited first, 26 of 26)

- [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)
- [A Sharper Global Convergence Analysis for Average Reward Reinforcement Learning via an Actor-Critic Approach](https://mlsanity.com/paper/2407.18878/) (2024)
- [Order-Optimal Regret with Novel Policy Gradient Approaches in Infinite-Horizon Average Reward MDPs](https://mlsanity.com/paper/2404.02108/) (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)
- [On the Global Convergence of Policy Gradient in Average Reward Markov Decision Processes](https://mlsanity.com/paper/2403.06806/) (2024)
- [Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm](https://mlsanity.com/paper/2505.15138/) (2025)
- [Finite-Sample Analysis of Policy Evaluation for Robust Average Reward Reinforcement Learning](https://mlsanity.com/paper/2502.16816/) (2025)
- [Regret Analysis of Average-Reward Unichain MDPs via an Actor-Critic Approach](https://mlsanity.com/paper/2505.19986/) (2025)
- [Towards Global Optimality for Practical Average Reward Reinforcement Learning without Mixing Time Oracles](https://mlsanity.com/paper/2403.11925/) (2024)
- [Efficient Q-Learning and Actor-Critic Methods for Robust Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2506.07040/) (2025)
- [Why Policy Gradient Algorithms Work for Undiscounted Total-Reward MDPs](https://mlsanity.com/paper/2510.18340/) (2025)
- [Regret Analysis of Unichain Average Reward Constrained MDPs with General Parameterization](https://mlsanity.com/paper/2602.08000/) (2026)
- [Quantum Speedups in Regret Analysis of Infinite Horizon Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2310.11684/) (2023)
- [Sample Complexity of Average-Reward Q-Learning: From Single-agent to Federated Reinforcement Learning](https://mlsanity.com/paper/2601.13642/) (2026)
- [Policy Gradient Algorithms in Average-Reward Multichain MDPs](https://mlsanity.com/paper/2602.18003/) (2026)
- [Learning Policy from a Single Trajectory in Average-Reward Markov Decision Process](https://mlsanity.com/paper/2606.16729/) (2026)
- [Anytime Safe Reinforcement Learning](https://mlsanity.com/paper/2504.16417/) (2025)
- [Finite-Time Bounds for Average-Reward Fitted Q-Iteration](https://mlsanity.com/paper/2510.17391/) (2025)
- [Learning Weakly Communicating Average-Reward CMDPs: Strong Duality and Improved Regret](https://mlsanity.com/paper/2605.11586/) (2026)
- [Last-Iterate Convergence of General Parameterized Policies in Constrained MDPs](https://mlsanity.com/paper/2408.11513/) (2024)
- [Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterization](https://mlsanity.com/paper/2602.11387/) (2026)
- [Natural Policy Gradient for Average Reward Non-Stationary RL](https://mlsanity.com/paper/2504.16415/) (2025)
- [Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow](https://mlsanity.com/paper/2510.01492/) (2025)
- [Bias-Controlled Primal-Dual Natural Actor-Critic: Optimal Rates for Constrained Multi-Objective Average-Reward RL](https://mlsanity.com/paper/2606.25012/) (2026)
- [High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence](https://mlsanity.com/paper/2606.26316/) (2026)
- [Sharp Convergence and Sample Complexity of Policy Mirror Descent for Average-Reward MDPs](https://mlsanity.com/paper/2610.04117/) (2026)

## Abstract (arXiv)

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has tildeO(T3/4) regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret-bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.