Variance-Reduced Policy Gradient Approaches for Improving Regret Bounds in Infinite Horizon Average Reward Markov Decision Processes

Core Concepts

We present two policy gradient-based algorithms that achieve improved regret bounds compared to the state-of-the-art for infinite horizon average reward Markov Decision Processes with general policy parameterization.

Abstract

The paper presents two policy gradient-based algorithms for solving infinite horizon average reward Markov Decision Processes (MDPs) with general policy parameterization.
Key highlights:

The first algorithm employs implicit gradient transport for variance reduction, achieving a regret bound of order ~O(T^{3/5}).
The second algorithm utilizes a Hessian-based technique, attaining a regret bound of order ~O(√T), which is optimal.
These results significantly improve upon the existing state-of-the-art regret bound of ~O(T^{3/4}).
The authors address technical challenges in adapting variance reduction techniques from the discounted reward setup to the average reward setup.
The algorithms only require sampling a single trajectory per iteration and have similar memory and computational complexity to Hessian-free methods.
The paper first provides an overview of related work in policy gradient methods for discounted reward MDPs and model-based/tabular approaches for average reward MDPs. It then introduces the problem setup and key assumptions.
The two proposed algorithms are then described in detail:

Parameterized Policy Gradient with Implicit Gradient Transport:

Utilizes implicit gradient transport for variance reduction without requiring importance sampling or curvature information.
Achieves a regret bound of order ~O(T^{3/5}).

Parameterized Hessian-aided Policy Gradient:

Incorporates second-order information via Hessian estimates.
Attains a regret bound of order ~O(√T), which is optimal.

The paper provides a detailed proof outline, establishing key lemmas on the properties of the gradient and Hessian estimators, as well as bounds on the expected regret for both algorithms.

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Key Insights Distilled From

Variance-Reduced Policy Gradient Approaches for Infinite Horizon Average Reward Markov Decision Processes

by Swetha Ganes... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.02108.pdf

Deeper Inquiries

How can the proposed algorithms be extended to handle constrained Markov Decision Processes with average reward criteria

To extend the proposed algorithms to handle constrained Markov Decision Processes (MDPs) with average reward criteria, we can incorporate the constraints into the optimization problem. This can be achieved by adding the constraints as additional terms in the objective function that the algorithm aims to optimize. The constraints can be formulated based on the specific requirements of the constrained MDPs, such as limiting the actions or states based on certain conditions.
In the context of the proposed algorithms, we would need to modify the policy gradient updates to ensure that the constraints are satisfied during the learning process. This may involve adjusting the gradient calculations to account for the constraints and incorporating them into the optimization procedure. By incorporating the constraints into the algorithm, we can ensure that the learned policies adhere to the constraints while optimizing for the average reward criteria.

What are the potential challenges in applying these variance reduction techniques to other reinforcement learning settings beyond average reward MDPs

Applying variance reduction techniques to other reinforcement learning settings beyond average reward MDPs may pose several challenges. One key challenge is the adaptation of these techniques to different reward structures and optimization objectives. Variance reduction methods are often tailored to specific settings, and their effectiveness can vary based on the characteristics of the problem.
Another challenge is the scalability of variance reduction techniques to larger state and action spaces. As the complexity of the environment increases, the computational and memory requirements of these methods may become prohibitive. Ensuring that the variance reduction techniques remain efficient and effective in high-dimensional spaces is crucial for their applicability to a wide range of reinforcement learning problems.
Additionally, generalizing variance reduction techniques to different settings may require a deep understanding of the underlying dynamics of the environment. Adapting these methods to new contexts involves careful consideration of the specific challenges and requirements of the problem at hand to ensure that the techniques are appropriately applied and yield meaningful improvements in learning efficiency.

Can the ideas behind constructing the auxiliary function ¯J be leveraged to improve the sample complexity of policy gradient methods in other reinforcement learning frameworks

The construction of the auxiliary function ¯J can indeed be leveraged to improve the sample complexity of policy gradient methods in other reinforcement learning frameworks. By carefully designing an auxiliary function that captures the key properties of the optimization problem, we can potentially enhance the convergence properties and efficiency of policy gradient algorithms in various settings.
One approach could involve customizing the construction of ¯J to suit the specific characteristics of different reinforcement learning frameworks. By tailoring the auxiliary function to the unique features of the problem, we can potentially reduce the sample complexity and improve the learning efficiency of policy gradient methods.
Furthermore, leveraging the insights gained from constructing ¯J in the context of average reward MDPs, we can explore similar strategies in other reinforcement learning frameworks to enhance the performance of policy gradient algorithms. This may involve adapting the construction of auxiliary functions to address the challenges and requirements of different environments, ultimately leading to more effective and efficient learning algorithms.