By employing the Optimal Bayesian Robust (OBR) policy, Bayesian Markov Decision Process (BMDP) can be used to solve the Gene Regulatory Network (GRN) control problem. However, due to the "curse of dimensionality", the data storage limitation hinders the practical applicability of the BMDP. To overcome this impediment, we propose a novel Duplex Sparse Storage (DSS) scheme in this paper, and develop a BMDP solver with the DSS scheme on a heterogeneous GPU-based platform. The simulation results demonstrate that our approach achieves a 5x reduction in memory utilization with a 2.4% "decision difference" and an average speedup of 4.1x compared to the full matrix based storage scheme. Additionally, we present the tradeoff between the runtime and result accuracy for our DSS techniques versus the full matrix approach. We also compare our results with the well known Compressed Sparse Row (CSR) approach for reducing memory utilization, and discuss the benefits of DSS over CSR.