A Geometric Nash Approach in Tuning the Learning Rate in Q-Learning Algorithm

Abstract

This paper proposes a geometric approach for estimating the $\alpha$ value in Q learning. We establish a systematic framework that optimizes the {\alpha} parameter, thereby enhancing learning efficiency and stability. Our results show that there is a relationship between the learning rate and the angle between a vector T (total time steps in each episode of learning) and R (the reward vector for each episode). The concept of angular bisector between vectors T and R and Nash Equilibrium provide insight into estimating $\alpha$ such that the algorithm minimizes losses arising from exploration-exploitation trade-off.