Stabilizing Extreme Q-learning by Maclaurin Expansion

In Extreme Q-learning (XQL), Gumbel Regression is performed with an assumed Gumbel distribution for the error distribution. This allows learning of the value function without sampling out-of-distribution actions and has shown excellent performance mainly in Offline RL. However, issues remained, including the exponential term in the loss function causing instability and the potential for an error distribution diverging from the Gumbel distribution. Therefore, we propose Maclaurin Expanded Extreme Q-learning to enhance stability. In this method, applying Maclaurin expansion to the loss function in XQL enhances stability against large errors. It also allows adjusting the error distribution assumption from normal to Gumbel based on the expansion order. Our method significantly stabilizes learning in Online RL tasks from DM Control, where XQL was previously unstable. Additionally, it improves performance in several Offline RL tasks from D4RL, where XQL already showed excellent results.