XGBoost is a scalable machine learning system for tree boosting. Its objective function has a training loss and a regularization term: $L={\sum }_{i}l({}^{},{\hat{y}}_i)+{\sum }_k\Omega \left(f_k\right)$. Read the XGBoost paper and answer the following questions:

a. What is ${\hat{y}}_i$ ? At the $t$ th iteration, XGBoost fixes $f_1,\dots ,f_{t-\mathrm{(}}$ and trains the $t$ th tree model $f_t$. How does XGBoost approximate the training $\mathrm{loss})(y_i,{\hat{y}}_i)$ here?

b. What is $\Omega \left(f_k\right)$ ? Which part in the regularization term needs to be considered at the $t$ th iteration?