Modern recommender systems are built upon computation-intensive infrastructure, and it is challenging to perform real-time computation for each request, especially in peak periods, due to the limited computational resources. Recommending by user-wise result caches is widely used when the system cannot afford a real-time recommendation. However, it is challenging to allocate real-time and cached recommendations to maximize the users' overall engagement. This paper shows two key challenges to cache allocation, i.e., the temporal dependency and the streaming allocation. Then, we propose a reinforcement prediction-allocation framework (RPAF) to address these issues. RPAF is a reinforcement-learning-based two-stage framework containing prediction and allocation stages. The prediction stage estimates the values of the cache choices considering the strategy and value dependencies, while the allocation stage determines the cache choices for each request. We show that the challenge of training RPAF includes globality and the strictness of budget constraints, and a relaxed local allocator (RLA) is proposed to address this issue. Moreover, a PoolRank algorithm is used in the allocation stage to deal with the streaming allocation problem. Experiments show that RPAF significantly improves users' engagement under computational budget constraints.