Mobile Edge Computing plays a crucial role in supporting latency-sensitive and resource-intensive applications by processing tasks closer to end users. However, efficiently managing task offloading while minimizing energy consumption remains a significant challenge. This study explores AI-driven optimization for energy-efficient task offloading in Mobile Edge Computing (MEC), focusing on Multi-Armed Bandit (MAB) and Deep Q-Network (DQN) algorithms. MAB models dynamically allocate resources to balance exploration and exploitation, while DQNs learn adaptive policies to respond to changing workloads. Simulation results demonstrate that these AI techniques significantly improve energy efficiency compared to traditional methods, highlighting their potential for scalable, sustainable MEC systems.