A recently developed approach to precision medicine is the use of Markov Decision Processes (MDPs) on Gene Regulatory Networks (GRNs). Due to very limited information on the system dynamics of GRNs, the MDP must repeatedly conduct exhaustive search for a non-stationary policy, and thus entails exponential computational complexity. This has hindered its practical applications to date. With the goal of overcoming this obstacle, we investigate acceleration techniques, using the Graphic Processing Unit (GPU) platform, which allows massive parallelism. Our GPU-based acceleration techniques are applied with two different MDP approaches: the optimal Bayesian robust (OBR) policy and the forward search sparse sampling (FSSS) method. Simulation results demonstrate that our techniques achieve a speedup of two orders of magnitude over sequential implementations. In addition, we present a study on the memory utilization and error trends of these techniques.