Batch Gradient Descent Mini-Batch Gradient Descent and Stochastic Gradient Descent

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batch gradient descent
理想状态下经过足够多的迭代后可以达到全局最优。
很难处理大数据集

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X = data_input
Y = labels
parameters = initialize_parameters(layers_dims)
for i in range(0, num_iterations): #num_iterations--迭代次数
    # Forward propagation
    a, caches = forward_propagation(X, parameters)
    # Compute cost.
    cost = compute_cost(a, Y)
    # Backward propagation.
    grads = backward_propagation(a, caches, parameters)
    # Update parameters.
    parameters = update_parameters(parameters, grads)

stochastic gradient descent
每次也可以训练一小批样本
随机性避免陷入局部最优，但是每次更新方向会在总体的梯度向量方向上震荡。
和遗传算法有点像

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X = data_input
Y = labels
permutation = list(np.random.permutation(m))
shuffled_X = X[:, permutation]
shuffled_Y = Y[:, permutation].reshape((1, m))
for i in range(0, num_iterations):
    for j in range(0, m):  # 每次训练一个样本
        # Forward propagation
        AL,caches = forward_propagation(shuffled_X[:, j].reshape(-1,1), parameters)
        # Compute cost
        cost = compute_cost(AL, shuffled_Y[:, j].reshape(1,1))
        # Backward propagation
        grads = backward_propagation(AL, shuffled_Y[:,j].reshape(1,1), caches)
        # Update parameters.
        parameters = update_parameters(parameters, grads, learning_rate)

Mini-batch gradient descent
batch_size =m = 2 ** n
深度学习基本都用 Mini-batch gradient descent
SGD = stochastic mini-batch gradient descent

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# GRADED FUNCTION: random_mini_batches
def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):
    """
    Creates a list of random minibatches from (X, Y)
    Arguments:
    X -- input data, of shape (input size, number of examples)
    Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
    mini_batch_size -- size of the mini-batches, integer

    Returns:
    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)
    """
    np.random.seed(seed)            # To make your "random" minibatches the same as ours
    m = X.shape[1]                  # number of training examples
    mini_batches = []

    # Step 1: Shuffle (X, Y)
    permutation = list(np.random.permutation(m))
    shuffled_X = X[:, permutation]
    shuffled_Y = Y[:, permutation].reshape((1,m))

    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.
    num_complete_minibatches = m//mini_batch_size # number of mini batches
    for k in range(0, num_complete_minibatches):
        mini_batch_X = shuffled_X[:, k * mini_batch_size: (k + 1) * mini_batch_size]
        mini_batch_Y = shuffled_Y[:, k * mini_batch_size: (k + 1) * mini_batch_size]
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)

    # Handling the end case (last mini-batch < mini_batch_size)
    if m % mini_batch_size != 0:
        mini_batch_X = shuffled_X[:, num_complete_minibatches * mini_batch_size : m]
        mini_batch_Y = shuffled_Y[:, num_complete_minibatches * mini_batch_size : m]
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)

    return mini_batches
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seed = 0
for i in range(0, num_iterations):
    # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch
    seed = seed + 1
    minibatches = random_mini_batches(X, Y, mini_batch_size, seed)
    for minibatch in minibatches:
        # Select a minibatch
        (minibatch_X, minibatch_Y) = minibatch
        # Forward propagation
        AL, caches = forward_propagation(minibatch_X, parameters)
        # Compute cost
        cost = compute_cost(AL, minibatch_Y)
        # Backward propagation
        grads = backward_propagation(AL, minibatch_Y, caches)
        parameters = update_parameters(parameters, grads, learning_rate)

超参数batch_size