Q-Learning for Continuous State and Action MDPs under Average Cost Criteria

Основні поняття

New approximation and reinforcement learning results for continuous state and action MDPs under average cost criteria.

Анотація

The content discusses approximation methods, Q-learning algorithms, convergence analysis, and near optimality results for Markov Decision Processes with continuous spaces under average cost criteria. It covers discretization-based approximations, synchronous and asynchronous Q-learning algorithms, convergence to optimal Q values, and the implications of these findings. The paper introduces new approaches and relaxation of continuity conditions compared to prior work.

Introduction

Discusses approximate solutions for MDPs under average cost criteria.
Focuses on problems with continuous state and action spaces.

Literature Review

Highlights various approximation techniques used in MDPs.
Discusses challenges in applying existing techniques to average cost problems with continuous spaces.

Finite Approximations

Quantization of state and action spaces for finite models.
Error bounds for approximations based on weak continuity conditions.

Quantized Q-Learning

Presents synchronous and asynchronous Q-learning algorithms.
Convergence analysis to optimal Q values for finite models constructed via quantization.

Conclusions

Summarizes contributions regarding near optimality of quantized models under average cost criteria.

Статистика

For infinite-horizon average-cost criterion problems, there are few rigorous approximation results.
The paper presents discretization-based approximation methods for fully observed MDPs with continuous spaces.
Synchronous and asynchronous Q-learning algorithms are provided for continuous spaces via quantization.

Цитати

"There exist relatively few rigorous approximation and reinforcement learning results."
"Our Q-learning convergence results are new for continuous spaces."

Ключові висновки, отримані з

Q-Learning for Continuous State and Action MDPs under Average Cost Criteria

by Ali Devran K... о arxiv.org 03-20-2024

https://arxiv.org/pdf/2308.07591.pdf

Глибші Запити

How do weak continuity conditions impact the accuracy of approximations

Weak continuity conditions impact the accuracy of approximations by influencing the convergence and stability of the algorithms used for approximation. In the context of Q-learning for continuous spaces under average cost criteria, weak continuity conditions allow for more flexibility in modeling complex systems with continuous state and action spaces. By relaxing strong continuity requirements, weak continuity enables a broader range of applications where exact mathematical precision may not be feasible or necessary. However, weaker continuity conditions may also introduce errors or uncertainties in the approximation process, potentially affecting the optimality and convergence guarantees provided by the algorithms.

What are the implications of relaxing total variation continuity assumptions

Relaxing total variation continuity assumptions has significant implications for improving the applicability and robustness of models in practical settings. Total variation continuity is a stringent requirement that limits the types of problems that can be effectively addressed using traditional methods. By relaxing this assumption to weaker forms such as weak or Wasserstein continuity, it becomes possible to tackle a wider class of problems with continuous spaces under average cost criteria. This relaxation allows for more realistic representations of real-world systems that may exhibit varying degrees of smoothness or regularity in their dynamics.

How can these findings be applied to real-world scenarios beyond theoretical models

The findings regarding weak continuity conditions and relaxed total variation assumptions have important implications for real-world scenarios beyond theoretical models. These advancements enable more accurate modeling and analysis of complex systems with continuous state and action spaces in various fields such as robotics, finance, healthcare, transportation, and environmental management. For example:

In autonomous robotics applications: Weakly continuous approximations can enhance path planning algorithms by providing smoother trajectories while ensuring near-optimal performance.
In financial risk management: Relaxing total variation assumptions allows for better estimation of portfolio returns under uncertain market conditions.
In healthcare optimization: Models based on Wasserstein continuity can improve resource allocation strategies in hospitals to optimize patient care outcomes.
Overall, these findings open up new possibilities for applying reinforcement learning techniques to address challenging problems across diverse industries where precise control decisions are required within dynamic environments characterized by continuous variables.