Batch Gradient Descent vs Mini-Batch Gradient Descent vs Stochastic gradient descent

Batch Gradient Descent

• Each step of gradient descent uses all the training examples.
• Advantage: Achieve global optimum after enough iteration.
• Disadvantage: Large data set. Computationally expensive, or even fail to complete.

Stochastic Gradient Descent

• Each step uses one training example.
• Learning rate $\alpha$α is typically held constant. Can slowly decrease $\alpha$α over time is we want $\theta$θ to converge
  
• Advantage: Robot for large data set.
• Disadvantage: Unstable. Move “around” to the optimum, not go straight to the optimum(Batch).
• NOTE: Shuffling is really important. To avoid ending up at local optimum.
  

Mini-batch Gradient Descent

• Combine Batch with Stochastic: Use b examples in each iteration. Batch size
• More smoothly, compared to Stochastic.
• Additional parameter: batch_size