The integration of machine learning models in various real-world applications is becoming more prevalent to assist humans in their daily decision-making tasks as a result of recent advancements in this field. However, it has been discovered that there is a tradeoff between the accuracy and fairness of these decision-making tasks. In some cases, these AI systems can be unfair by exhibiting bias or discrimination against certain social groups, which can have severe consequences in real life. Inspired by one of the most well-known human learning skills called grouping, we address this issue by proposing a novel machine learning (ML) framework where the ML model learns to group a diverse set of problems into distinct subgroups to solve each subgroup using its specific sub-model. Our proposed framework involves three stages of learning, which are formulated as a three-level optimization problem: 1) grouping problems into subgroups, 2) learning group-specific sub-models for problem-solving, and 3) updating group assignments of training examples by minimizing validation loss. These three learning stages are performed end-to-end in a joint manner using gradient descent. To improve fairness and accuracy, we develop an efficient optimization algorithm to solve this three-level optimization problem. To further decrease the risk of overfitting in small datasets using our LBG method, we incorporate domain adaptation techniques in the second stage of training. We further apply our method to differentiable neural architecture search (NAS) methods.