  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 \cite{massart2006risk}), and emphasize the
impact of cost terms on the hardness.
