Generalized Speedy Q-learning

TL;DR

This paper introduces a generalized version of the Speedy Q-learning algorithm, utilizing a relaxed Bellman operator to improve convergence speed and finite-time performance in reinforcement learning tasks.

Contribution

It proposes the GSQL-w algorithm, a novel family of algorithms based on generalized Bellman operators, with proven improved finite-time bounds over traditional SQL.

Findings

GSQL-w outperforms SQL in finite-time performance.

The generalized Bellman operator has a smaller contraction factor.

Numerical experiments confirm empirical improvements.

Abstract

In this paper, we derive a generalization of the Speedy Q-learning (SQL) algorithm that was proposed in the Reinforcement Learning (RL) literature to handle slow convergence of Watkins' Q-learning. In most RL algorithms such as Q-learning, the Bellman equation and the Bellman operator play an important role. It is possible to generalize the Bellman operator using the technique of successive relaxation. We use the generalized Bellman operator to derive a simple and efficient family of algorithms called Generalized Speedy Q-learning (GSQL-w) and analyze its finite time performance. We show that GSQL-w has an improved finite time performance bound compared to SQL for the case when the relaxation parameter w is greater than 1. This improvement is a consequence of the contraction factor of the generalized Bellman operator being less than that of the standard Bellman operator. Numerical experiments are provided to demonstrate the empirical performance of the GSQL-w algorithm.