Power saving is a main pillar in the operation of wireless communication systems. In this paper, we investigate cloud radio access network (C-RAN) capability to reduce power consumption based on the user equipment (UE) requirement. Aiming to save the long-term C-RAN energy consumption, an optimization problem is formulated to manage the downlink power without degrading the UE requirement by designing the power offset parameter. Considering stochastic traffic arrivals at UEs, we first formulate the problem as a Markov decision process (MDP) and then set up a dual objective optimization problem in terms of the downlink throughput and power. To solve this optimization problem, we develop a novel static deep Q-learning (SDQL) algorithm to maximize the downlink throughput and minimize the downlink power. In our proposed algorithm, we design multi-Q-tables to simultaneously optimize power reductions of activated RRHs by assigning one Q-table for each UE. To maximize the accumulative reward in terms of the downlink throughput loss and power reduction, our proposed algorithm performs power reductions of activated RRHs through continuous environmental interactions. Simulation results1 show that our proposed algorithm enjoys a superior average power reduction compared to the activation and sleep schemes, and enjoys a low computational complexity.