Recommender systems aim to recommend the most suitable items to users from a large number of candidates. Their computation cost grows as the number of user requests and the complexity of services (or models) increases. Under the limitation of computation resources (CRs), how to make a trade-off between computation cost and business revenue becomes an essential question. The existing studies focus on dynamically allocating CRs in queue truncation scenarios (i.e., allocating the size of candidates), and formulate the CR allocation problem as an optimization problem with constraints. Some of them focus on single-phase CR allocation, and others focus on multi-phase CR allocation but introduce some assumptions about queue truncation scenarios. However, these assumptions do not hold in other scenarios, such as retrieval channel selection and prediction model selection. Moreover, existing studies ignore the state transition process of requests between different phases, limiting the effectiveness of their approaches. This paper proposes a Reinforcement Learning (RL) based Multi-Phase Computation Allocation approach (RL-MPCA), which aims to maximize the total business revenue under the limitation of CRs. RL-MPCA formulates the CR allocation problem as a Weakly Coupled MDP problem and solves it with an RL-based approach. Specifically, RL-MPCA designs a novel deep Q-network to adapt to various CR allocation scenarios, and calibrates the Q-value by introducing multiple adaptive Lagrange multipliers (adaptive-$λ$) to avoid violating the global CR constraints. Finally, experiments on the offline simulation environment and online real-world recommender system validate the effectiveness of our approach.