Global Convergence Analysis of Policy Gradient in Average Reward MDPs

Core Concepts

The authors present the first finite-time global convergence analysis of policy gradient in average reward Markov decision processes, proving that the algorithm converges for average-reward MDPs with sublinear regret. Their primary contribution lies in obtaining finite-time performance guarantees.

Abstract

The content discusses the global convergence analysis of policy gradient in average reward Markov decision processes. It highlights the challenges faced due to the absence of a discount factor and lack of uniqueness in the average reward value function. The authors introduce a new analysis technique to prove smoothness and provide finite-time performance bounds. Simulations demonstrate faster convergence for MDPs with lower complexity.
Key points include:

Introduction to Average Reward MDPs and applications.
Challenges in analyzing policy gradient methods for average reward MDPs.
Smoothness analysis of the average reward function.
Sublinear convergence bounds and unique value function representation.
Extension to Discounted Reward MDPs and simulation results.

Stats

Our analysis shows that the policy gradient iterates converge at a sublinear rate of O(1/T), translating to O(log(T)) regret.
Prior work on discounted reward MDPs cannot be extended to average reward MDPs due to bounds growing proportional to the fifth power of the effective horizon.

Quotes

"Motivated by this observation, we reexamine and improve existing performance bounds for discounted reward MDPs."
"Our primary contribution is proving that the policy gradient algorithm converges for average-reward MDPs."

Key Insights Distilled From

On the Global Convergence of Policy Gradient in Average Reward Markov Decision Processes

by Navdeep Kuma... at arxiv.org 03-12-2024

https://arxiv.org/pdf/2403.06806.pdf

Deeper Inquiries

How does the absence of a discount factor impact the convergence behavior?

The absence of a discount factor in average reward Markov Decision Processes (MDPs) poses challenges for analyzing convergence behavior. Unlike discounted reward MDPs, where the discount factor serves as a source of contraction facilitating analysis, average reward MDPs lack this property. This absence leads to technical difficulties in proving convergence properties for algorithms like policy gradients. The smoothness and uniqueness issues associated with the average reward value function make it challenging to establish global convergence guarantees.

What implications do these findings have on real-world applications using policy gradients?

The findings regarding the global convergence of policy gradient methods in average reward MDPs have significant implications for real-world applications. Understanding that policy gradient iterates converge at a sublinear rate provides valuable insights into algorithm performance over time. These results can guide practitioners in selecting appropriate step sizes and tuning hyperparameters to achieve optimal policies efficiently.
In practical applications such as resource allocation, portfolio management, healthcare decision-making, and robotics control, knowing that policy gradient algorithms converge for average-reward scenarios is crucial. It allows stakeholders to leverage reinforcement learning techniques effectively without relying solely on discounted rewards or facing challenges related to infinite horizons.

How can these results be applied to other reinforcement learning algorithms beyond policy gradients?

The insights gained from analyzing the global convergence of policy gradient methods in average reward MDPs can be extended to other reinforcement learning algorithms beyond just policy gradients. By understanding how different factors affect convergence rates and performance bounds in this context, researchers can adapt similar analytical frameworks to assess the behavior of alternative algorithms.
For instance, one could explore how natural actor-critic methods or Q-learning approaches behave under an average-reward setting based on similar principles used in this study. By considering complexities specific to each algorithm and adapting concepts like smoothness analysis and directional derivatives across policies, researchers can enhance their understanding of various reinforcement learning techniques' behaviors under different reward structures.