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

TL;DR

This paper introduces a double SOR Q-learning algorithm that is model-free and less biased, extending it to deep reinforcement learning and demonstrating improved convergence and performance in various environments.

Contribution

It proposes a novel sample-based, model-free double SOR Q-learning algorithm that reduces bias and extends to large-scale deep RL applications.

Findings

Less biased than traditional SOR Q-learning

Effective in large-scale deep RL environments

Improved convergence in tabular and deep settings

Abstract

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.