The measurement of quality for regression models has long been a fundamental concern in statistical research. In classical regression setting, the proximity of f(X) to Y is typically evaluated using Mean Squared Error (MSE), which is sensitive to the scale of data and penalizes large errors through a quadratic function. By contrast, Mean Absolute Percentage Error (MAPE) uses relative terms for measurement. Consequently, MAPE is less sensitive to outliers and more consistent when comparing performance across different scales. When using MAPE as an alternative to MSE, it has been shown that an optimal MAPE model exists, and we can find a strongly consistent estimator of MAPE risk that converges to empirical risk minimization almost surely. Also, the optimal model under MAPE is equivalent to performing weighted Mean Absolute Error (MAE) regression. To further develop the existing conclusion, we investigate whether empirical regularized risk minimization can be shown to achieve Fisher consistent in MAPE framework.