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吴恩达 Andrew Ng

Mini-batch 梯度下降法

• 把巨大的数据集分成一个一个的小部分

• 5000000 examples, 1000 × 5000, X{

  1}...X{
  5000} X { 1 } . . . X { 5000 } $X^{\{1\}}...X^{\{5000\}}$ , $Y^{\{1\}}...Y^{\{5000\}}$

• epoch means a single pass through the training set

• Batch gradient descent’s cost decrease on every iteration

• Mini-batch gradient descent may not decrease on every iteration. It trends downwards, but it’s going to be a little bit noisier.

• mini-batch size = m: Batch gradient descent

• mini-batch size = 1: Stochastic gradient descent (随机梯度下降法)

  不会收敛，最终在最小值处波动

• 一般 mini-batch 大小为 64、128、256、512

Exponentially weighted averages (指数加权平均)

• $V_t=\beta V_{t-1}+(1-\beta)\theta_t$

• $V_t$ approximately average over $\frac{1}{1-\beta}$ items

• 迭代几次公式，展开递推式

• 初始化 $V_0=0$

• As for computation and memory efficiency, it’s a good choice.

Bias correction in exponentially weighted average

• during initial phase of estimating, make it more accurate

• $\frac{V_t}{1-\beta ^{\, t}}$

• oscillations 震荡，波动

Momentum (动量梯度下降法)

• ball rolling down a bowl

• 

• usually $\beta = 0.9$

RMSprop

root mean square prop

Adam optimization algorithm

Adaptive Moment Estimation

• 结合 Momentum 和 RMSprop

• 适用性广泛

• Hyperparameters:

  $\alpha :$ needs to be tuned, $\beta _1:0.9$ , $\beta _2:0.999$ , $\epsilon:10^{-8}$

Learning rate decay

随着迭代的增加，渐渐减小学习率

• $\alpha = \frac{1}{1+decay_rate\times iteration}\alpha_0$

• $\alpha=0.95^{\, epoch\_num}\alpha_0$

• $\alpha=\frac{k}{\sqrt{epoch\_num}}\alpha_0$

• discrete staircase

• manually controlling alpha (small model)

The problem of local optima

• saddle point 马鞍点
• 许多低维空间里的直觉在高维空间中并不适用，高维空间极少出现局部最优点
• 平稳区域(plateaus)会降低学习效率