Accelerated magnetic resonance imaging resorts to either Fourier-domain subsampling or better reconstruction algorithms to deal with fewer measurements while still generating medical images of high quality. Determining the optimal sampling strategy given a fixed reconstruction protocol often has combinatorial complexity. In this work, we apply double deep Q-learning and REINFORCE algorithms to learn the sampling strategy for dynamic image reconstruction. We consider the data in the format of time series, and the reconstruction method is a pre-trained autoencoder-typed neural network. We present a proof of concept that reinforcement learning algorithms are effective to discover the optimal sampling pattern which underlies the pre-trained reconstructor network (i.e., the dynamics in the environment). The code for replicating experiments can be found at https://github.com/zhishenhuang/RLsamp.