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目标函数:![1614044218548](assets/1614044218548.png) - 求偏导:![1614044234709](assets/1614044234709.png) -- 偏导等于0:![1614044250549](assets/1614044250549.png) +- 偏导等于0的最优解:![1614044250549](assets/1614044250549.png) + + + +### 梯度下降 + +#### 通俗理解 + +- 引入:当我们得到了一个目标函数后,如何求解?(并不一定可解,线性回归可以当做是一个特例) +- 常规套路:机器学习的套路就是我们交给机器一堆数据,然后告诉它什么样的学习方式是对的(目标函数),然后让它朝着这个方向去做 +- 如何优化:一步步的完成迭代。![1614051473653](assets/1614051473653.png) + +#### 参数更新方法 + +- 目标函数:![1614053992861](assets/1614053992861.png) + + > θ0和θ1分别得出方向,最终找到综合的结果。 + +- 寻找山谷的最低点,也就是我们的目标函数终点 + +- 下山分多步走(更新参数) + + 1. 找到最合适的方向 + 2. 每次走一小步 + 3. 按照方向和步伐更新参数 + +![1614054121928](assets/1614054121928.png) + +梯度下降,目标函数:![1614054304093](assets/1614054304093.png) + +- 批量梯度下降:![1614054320647](assets/1614054320647.png) + + (容易得到最优解,但由于每次考虑所有样本,速度很慢) + +- 随机梯度下降:![1614054359779](assets/1614054359779.png) + + (每次找到一个样本,迭代速度快,但不一定每次都朝着收敛的方向) + +- 小批量梯度下降发:![1614054402887](assets/1614054402887.png) + + (每次更新选择一小部分数据来算) + + + +#### 学习率(步长) + +> 上面小批量梯度公式里的α + +- 学习率(步长):对结果会产生巨大的影响,一般小一些 +- 如何选择:从小的开始,知道不能再小 +- 批处理数:32、64、128都可以,很多时候还要考虑资源和时间 + +![1614062404175](assets/1614062404175.png)