Minimax Lower Bounds for Cost Sensitive Classification

The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied extensively in the literature, the fundamental limits of this problem are still not well understood. We investigate the hardness of this problem by extending the standard minimax lower bound of balanced binary classification problem (due to citemassart2006risk), and emphasize the impact of cost terms on the hardness.