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arXiv 2409.06356cs.LGcs.AI
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双重逐次超松弛Q学习及其在深度强化学习中的扩展

Double Successive Over-Relaxation Q-Learning with an Extension to Deep Reinforcement Learning

Research Scholar, Department of Mathematics, Indian Institute of Technology (IIT) Indore(印度理工学院印度奥德分校数学系研究学者)

Shreyas S R

AI总结:

提出基于样本的无模型双重SOR Q学习算法,通过引入双重机制解决原算法的过高估计偏差与依赖转移概率的问题,并扩展至深度强化学习,在表格与OpenAI Gym环境中验证了有效性。

摘要:

Q学习是强化学习(RL)中广泛使用的算法,但其收敛可能很慢,特别是当折扣因子接近1时。逐次超松弛(SOR)Q学习通过引入松弛因子来加速收敛,解决了这一问题,但存在两个主要局限:在表格设定中,松弛参数依赖于转移概率,使其并非完全无模型;并且它存在过高估计偏差。为了克服这些局限,我们提出了一种基于样本的无模型双重SOR Q学习算法。在理论和经验上,该算法被证明比SOR Q学习偏差更小。此外,在表格设定中,讨论了在迭代有界假设下的收敛性分析。所提出的算法使用深度RL扩展到大规模问题。最后,所提算法的表格版本使用轮盘赌和网格世界环境进行了比较,而深度RL版本在最大化偏差示例和OpenAI Gym环境上进行了测试。

英文摘要:

Q-learning is a widely used algorithm in reinforcement learning (RL), but its convergence can be slow, especially when the discount factor is close to one. Successive Over-Relaxation (SOR) Q-learning, which introduces a relaxation factor to speed up convergence, addresses this issue but has two major limitations: In the tabular setting, the relaxation parameter depends on transition probability, making it not entirely model-free, and it suffers from overestimation bias. To overcome these limitations, we propose a sample-based, model-free double SOR Q-learning algorithm. Theoretically and empirically, this algorithm is shown to be less biased than SOR Q-learning. Further, in the tabular setting, the convergence analysis under boundedness assumptions on iterates is discussed. The proposed algorithm is extended to large-scale problems using deep RL. Finally, the tabular version of the proposed algorithm is compared using roulette and grid world environments, while the deep RL version is tested on a maximization bias example and OpenAI Gym environments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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