The monotonous nature of repetitive cognitive training may cause losing interest in it and dropping out by older adults. This study introduces an adaptive technique that enables a Socially Assistive Robot (SAR) to select the most appropriate actions to maintain the engagement level of older adults while they play the serious game in cognitive training. The goal is to develop an adaptation strategy for changing the robot's behaviour that uses reinforcement learning to encourage the user to remain engaged. A reinforcement learning algorithm was implemented to determine the most effective adaptation strategy for the robot's actions, encompassing verbal and nonverbal interactions. The simulation results demonstrate that the learning algorithm achieved convergence and offers promising evidence to validate the strategy's effectiveness.