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

This paper proposes a geometric approach for estimating the α value in Q learning. We establish a systematic framework that optimizes the α 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 α such that the algorithm minimizes losses arising from explorationexploitation trade-off. Keywords: Q Learning, Reinforcement Learning, Nash Equilibrium, Learning Rate, α, Stability of Equilibrium 1 - Introduction Reinforcement Learning (RL) algorithms, particularly Q-learning, are pivotal in enabling agents to learn optimal strategies through interaction with environments.