We have two tracks in this competition with different cost function.
Mean Absolute Error is a common evaluation criterion to measure the average magnitude of the errors, which doesn’t consider the direction. However, for a multi-target regression problem, mean absolute error may lead to a bias that only optimize the large target instead of the small. As a result, in this track, the error for each target would be multiplied with a weight. That is, $$ \text{WMAE}(Y, \hat{Y}) = \dfrac{1}{n_{samples}} \sum_{i=1}^{n_{samples}} \sum_{j=1}^{3} w_{j}|y_{ij} - \hat{y}_{ij}|$$ Where $\hat{Y}$ is the predicted value set and $y_{i}$ is the true value set. $n_{samples}$ means the number of testing samples. In this track, w is 300 for penetration_rate, 1 for mesh_size and 200 for alpha.
In this track, we are going to use NAE to tackle the effect of scale in multi-target regression task. Normalized Absolute Error is defined as below $$ \text{NAE}(Y, \hat{Y}) = \dfrac{1}{n_{samples}} \sum_{i=1}^{n_{samples}} \sum_{j=1}^{3} \frac{|y_{ij} - \hat{y}_{ij}|} {y_{ij} } $$ Where $\hat{Y}$ is the predicted value set and $y_{i}$ is the true value set. $n_{samples}$ means the number of testing samples.