To extend the proposed framework to consider dynamic user preferences and content popularities over time, we can introduce a learning component that continuously updates the models based on real-time data. This can involve implementing reinforcement learning techniques to adapt to changing user behaviors and content trends. By incorporating feedback mechanisms that capture user interactions and content popularity shifts, the system can dynamically adjust its caching and recommendation strategies. Additionally, integrating algorithms that can handle non-stationary environments, such as online learning algorithms or contextual bandit approaches, can help in capturing the evolving user preferences and content popularity patterns over time.