# 2.10 局部最优的问题(The problem of local optima)

以前对局部最优解的理解是形如碗状的凹槽，如下图左边所示。但是在神经网络中，local optima的概念发生了变化。大部分梯度为零的“最优点”并不是这些凹槽处，而是形如右边所示的马鞍状，称为saddle point（鞍点）。即梯度为零并不能保证都是convex（极小值），也有可能是concave（极大值）。特别是在神经网络中参数很多的情况下，所有参数梯度为零的点很可能都是右边所示的马鞍状的saddle point，而不是左边那样的local optimum

![](/files/-Le0caq5ZKEkUCXG7ghi)

类似马鞍状的plateaus（平稳端）会降低神经网络学习速度。Plateaus是梯度接近于零的平缓区域，在plateaus上梯度很小，前进缓慢，到达saddle point需要很长时间。到达saddle point后，由于随机扰动，梯度一般能够沿着图中绿色箭头，离开saddle point，继续前进，只是在plateaus上花费了太多时间

![](/files/-Le0caq7f6gGiBMuzy3V)

local optima的两点总结：

* **只要选择合理的强大的神经网络，一般不太可能陷入local optima**
* **Plateaus可能会使梯度下降变慢，降低学习速度**

动量梯度下降，RMSprop，Adam算法都能有效解决plateaus下降过慢的问题，大大提高神经网络的学习速度


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