Resistive random-access memory (ReRAM) is a promising technology for designing hardware accelerators for deep neural network (DNN) inferencing. However, stochastic noise in ReRAM crossbars can degrade the DNN inferencing accuracy. We propose the design and optimization of a high-performance, area-and energy-efficient ReRAMbased hardware accelerator to achieve robust DNN inferencing in the presence of stochastic noise. We make two key technical contributions. First, we propose a stochastic-noise-aware training method, referred to as ReSNA, to improve the accuracy of DNN inferencing on ReRAM crossbars with stochastic noise. Second, we propose an informationtheoretic algorithm, referred to as CF-MESMO, to identify the Pareto set of solutions to trade-off multiple objectives, including inferencing accuracy, area overhead, execution time, and energy consumption. The main challenge in this context is that executing the ReSNA method to evaluate each candidate ReRAM design is prohibitive. To address this challenge, we utilize the continuous-fidelity evaluation of ReRAM designs associated with prohibitive high computation cost by varying the number of training epochs to trade-off accuracy and cost. CF-MESMO iteratively selects the candidate ReRAM design and fidelity pair that maximizes the information gained per unit computation cost about the optimal Pareto front. Our experiments on benchmark DNNs show that the proposed algorithms efficiently uncover high-quality Pareto fronts. On average, ReSNA achieves 2.57% inferencing accuracy improvement for ResNet20 on the CIFAR-10 dataset with respect to the baseline configuration. Moreover, CF-MESMO algorithm achieves 90.91% reduction in computation cost compared to the popular multi-objective optimization algorithm NSGA-II to reach the best solution from NSGA-II.