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Learning General Parameterized Policies for Infinite Horizon Average Reward Constrained MDPs via Primal-Dual Policy Gradient Algorithm


Core Concepts
This paper introduces a novel policy gradient algorithm for infinite horizon average reward constrained Markov Decision Processes (CMDPs) with general parameterization, achieving sublinear regret and constraint violation bounds.
Abstract
This paper explores the realm of infinite horizon average reward Constrained Markov Decision Processes (CMDP) with a focus on regret and constraint violation analysis. The proposed primal-dual based policy gradient algorithm manages constraints effectively while ensuring low regret towards achieving an optimal policy. The study bridges the gap in regret and constraint violation analysis for average reward CMDPs with general parametrization, providing significant advancements in the field of reinforcement learning. The framework of Reinforcement Learning (RL) is discussed, emphasizing the significance of infinite horizon average reward setup for real-world applications. The paper addresses challenges in solving CMDP problems using model-based and model-free approaches, highlighting the importance of general parameterization to accommodate large state spaces efficiently. The proposed algorithm achieves sub-linear regret and constraint violation bounds, improving upon existing state-of-the-art results. Key algorithms and their performance metrics are summarized in a table, showcasing the advancements made by the proposed primal-dual policy gradient algorithm. The convergence analysis, global convergence results, and detailed formulation provide insights into the effectiveness of the algorithm in handling complex reinforcement learning problems.
Stats
˜O(T 4/5) ˜O(T 4/5)
Quotes
"We propose a PG-based algorithm with general parameterized policies for the average reward CMDP." "Our work improves the state-of-the-art regret guarantee in model-free tabular setup."

Deeper Inquiries

How does the proposed primal-dual policy gradient algorithm compare to existing methods in terms of computational efficiency

The proposed primal-dual policy gradient algorithm offers several advantages in terms of computational efficiency compared to existing methods. One key aspect is the utilization of general parameterization, allowing for policies indexed by finite-dimensional parameters such as neural networks. This enables the algorithm to handle large state spaces efficiently by updating these parameters using policy gradient-type algorithms. Additionally, the algorithm's approach to managing constraints while ensuring low regret guarantees towards achieving an optimal policy contributes to its computational efficiency. Furthermore, the use of a sample trajectory length and sub-trajectories helps reduce bias in estimations, leading to more accurate updates and improved convergence rates. The careful choice of learning rates also plays a crucial role in balancing regret reduction and constraint violation minimization effectively. By incorporating these strategies, the primal-dual policy gradient algorithm demonstrates enhanced computational efficiency in tackling infinite horizon average reward constrained Markov Decision Processes (CMDPs).

What implications does the assumption of ergodicity have on the convergence results of the algorithm

The assumption of ergodicity significantly impacts the convergence results of the algorithm by providing essential properties that facilitate robust analysis and optimization within CMDPs. Ergodicity ensures that there exists a unique stationary distribution for every policy employed, which simplifies calculations related to value functions and transition probabilities. In terms of convergence results, ergodicity allows for establishing sublinear regret and constraint violation bounds with greater confidence due to stable long-term behavior guaranteed by this property. It ensures that trajectories explore all states sufficiently over time, leading to reliable estimates and effective learning processes within CMDPs. Moreover, ergodicity supports theoretical analyses regarding mixing times and hitting times necessary for bounding regrets and violations accurately. By assuming ergodicity in CMDPs as done in this context, researchers can derive rigorous convergence guarantees essential for developing efficient reinforcement learning algorithms.

How can these findings be applied to real-world scenarios beyond traditional reinforcement learning environments

The findings from this research have significant implications beyond traditional reinforcement learning environments when applied to real-world scenarios requiring decision-making under constraints with long-term goals or objectives. Epidemic Control: In epidemic control scenarios like disease spread management or vaccination policies where budget constraints need consideration alongside maximizing rewards (e.g., minimizing infections), applying constrained Markov Decision Processes with average reward settings can help optimize resource allocation efficiently while meeting cost limitations. Financial Portfolio Management: Utilizing similar techniques could aid financial institutions in portfolio management decisions where maintaining certain risk thresholds or investment limits is crucial along with maximizing returns over extended periods. Supply Chain Optimization: For supply chain logistics involving inventory management or production planning under capacity constraints or cost restrictions while aiming at optimizing operational efficiencies over time horizons; leveraging advanced reinforcement learning algorithms tailored for average reward CMDPs can lead to better decision-making outcomes. By integrating these research insights into practical applications across various domains beyond traditional RL settings, organizations can enhance their strategic planning processes while considering complex trade-offs between rewards and constraints effectively over extended durations.
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