We have already entered the heterogeneous computing era when computing systems harness computational horsepower from not only general purpose CPUs but also other processors such as graphics processing unit (GPU) and hardware accelerators. Performance, power-efficiency, and reliability are three most critical aspects of processors, and there usually exists a tradeoff among them. Accelerators are heavily optimized for performance and power-efficiency rather than reliability. However, it is equally important to ensure overall reliability while introducing accelerators to computing systems. In this paper, we focus on optimizing accelerator’s reliability without adopting the “whac-a-mole” paradigm which develops accelerator-specific reliability optimization. Instead, we advocate maintaining the reliability at the system level, and propose the design paradigm called “asymmetric resilience,” whose principle is to develop the reliable heterogeneous system centering around the CPU architecture. This generic design paradigm eases accelerators away from reliability optimization. We present the design principles and practices for the heterogeneous system that adopt such design paradigm. Following the principles of asymmetric resilience, we demonstrate how to use CPU architecture to handle GPU execution errors, which allows GPU focus on typical case operation for better energy efficiency. We explore the design space and show that the average overhead is only 1% for error-free execution and the overhead increases linearly with error probability.