将\(L(y_i,f(x_i))\)在\(f(x_i)=f_{m-1}(x_i)\)处泰勒展开到一阶（舍去余项，故为近似）
\[L(y_i,f(x_i))\approx L(y_i,f_{m-1}(x_i))+\left. \frac{\partial L(y_i,f(x_i))}{\partial f(x_i)} \right|_{f(x_i)=f_{m-1}(x_i)}\cdot (f(x_i)-f_{m-1}(x_i))
\]
令\(f(x_i) = f_{m-1}(x_i)\)且\(f_m(x_i) = f_{m-1}(x_i)+T_m(x_i;\theta _m)\)带入上式并移项
\[L(y_i,f_m(x_i))-L(y_i,f_{m-1}(x_i))\approx \left. \frac{\partial L(y_i,f(x_i))}{\partial f(x_i)} \right|_{f(x_i)=f_{m-1}(x_i)}\cdot T_m(x_i;\theta _m)
\]
左式需小于0（每轮得到的强学习器需要比上一轮强学习器在损失函数更小，不然优化无意义），故令\(T_m(x_i;\theta _m)\)去拟合\(-\left. \frac{\partial L(y_i,f(x_i))}{\partial f(x_i)} \right|_{f(x_i)=f_{m-1}(x_i)}\)使得右式小于0。
混淆点：\(f(x_i)\)是一个变量，代表最终求得的强学习器在第\(i\)个样本\(x_i\)上的预测，\(f_{m-1}(x_i)\)和\(f_m(x_i)\)是常量，即\((m-1)\)轮和\(m\)轮得到的强学习器在样本\(x_i\)上的预测
