C2W2_Assignment_Optimization+methods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * grads[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k*mini_batch_size : (k+1)*mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k*mini_batch_size : (k+1)*mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, num_complete_minibatches*mini_batch_size:]\n",
    "        mini_batch_Y = shuffled_Y[:, num_complete_minibatches*mini_batch_size:]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta * v[\"dW\" + str(l+1)] + (1 - beta) * grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta * v[\"db\" + str(l+1)] + (1 - beta) * grads['db' + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1 * v[\"dW\" + str(l+1)] + (1 - beta1) * grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1 * v[\"db\" + str(l+1)] + (1 - beta1) * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)] / (1 - beta1**t)\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)] / (1 - beta1**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2 * s[\"dW\" + str(l+1)] + (1 - beta2) * (grads[\"dW\" + str(l+1)])**2\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\" + str(l+1)] + (1 - beta2) * (grads[\"db\" + str(l+1)])**2\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)] / (1 - beta2**t)\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)] / (1 - beta2**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v_corrected[\"dW\" + str(l+1)] / (np.sqrt(s_corrected[\"dW\" + str(l+1)]) + epsilon)\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v_corrected[\"db\" + str(l+1)] / (np.sqrt(s_corrected[\"db\" + str(l+1)]) + epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09244991 -0.16498684]]\n",
      "b2 = [[-0.88529979]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n",
      "s[\"dW1\"] = [[ 0.00121136  0.00131039  0.00081287]\n",
      " [ 0.0002525   0.00081154  0.00046748]]\n",
      "s[\"db1\"] = [[  1.51020075e-05]\n",
      " [  8.75664434e-04]]\n",
      "s[\"dW2\"] = [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
      " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
      " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
      "s[\"db2\"] = [[  5.49507194e-05]\n",
      " [  2.75494327e-03]\n",
      " [  5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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pOWkUwU3qEtmtJb0/fpResx/xuC68Y1OfiT+B9aMuqz234tQsEn9ZR8qqHcgq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I8dQMdp/sebcSSfp+77GZdTx1HWW/bVJ1t48JmpxMSdCuKH9ufw9AO/4HR69TYL8ux8+OZ60lJy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\nv5qYYyZ0Z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7686cd240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690736\n",
      "Cost after epoch 1000: 0.685273\n",
      "Cost after epoch 2000: 0.647072\n",
      "Cost after epoch 3000: 0.619525\n",
      "Cost after epoch 4000: 0.576584\n",
      "Cost after epoch 5000: 0.607243\n",
      "Cost after epoch 6000: 0.529403\n",
      "Cost after epoch 7000: 0.460768\n",
      "Cost after epoch 8000: 0.465586\n",
      "Cost after epoch 9000: 0.464518\n"
     ]
    },
    {
     "data": {
      "image/png": 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wlqP9wbwuUpgT5yP9xTNK+yasgvvyLcOmajcjoVmSScVzpwwX6Qdu3ADAsQGj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\nzUrB63Lw1++8gruu7VzuraxorASY6dncMcPlGH1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mfIJzbta46qxlDOeMB549RGYol7jd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd73373ae80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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QUloyb2BY3dRC5J6ncEoKy5abWuwg6h15vIgMZcShw3WUzlwNIZ4QOrsOVpLNKTWP+3re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zz0/W/4jZ7NT8RL9+zphpLyC8fvLD5y+Ge6c/cWo2t75Ryjy1uMrlWbttjsLHQaW6pEE5fs0hml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\nioiIhFCiFBERCfH/50bmP+Yj+ssAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd733425358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690741\n",
      "Cost after epoch 1000: 0.685341\n",
      "Cost after epoch 2000: 0.647145\n",
      "Cost after epoch 3000: 0.619594\n",
      "Cost after epoch 4000: 0.576665\n",
      "Cost after epoch 5000: 0.607324\n",
      "Cost after epoch 6000: 0.529476\n",
      "Cost after epoch 7000: 0.460936\n",
      "Cost after epoch 8000: 0.465780\n",
      "Cost after epoch 9000: 0.464740\n"
     ]
    },
    {
     "data": {
      "image/png": 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0SxQthiuQHesa+bPbtnLrtvbiJ1eATW0BBoJRDvQH86ZIAS5qN4ptSkmV9k0Y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\n+OEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd73343de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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vH0vDbK0EVB2vC/msS6lYoj++v3Ntx3NzXOg/gZL6fabsNImQRb5hbJ5h2gpz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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd733778d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690552\n",
      "Cost after epoch 1000: 0.185567\n",
      "Cost after epoch 2000: 0.150852\n",
      "Cost after epoch 3000: 0.074454\n",
      "Cost after epoch 4000: 0.125936\n",
      "Cost after epoch 5000: 0.104235\n",
      "Cost after epoch 6000: 0.100552\n",
      "Cost after epoch 7000: 0.031601\n",
      "Cost after epoch 8000: 0.111709\n",
      "Cost after epoch 9000: 0.197648\n"
     ]
    },
    {
     "data": {
      "image/png": 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7HdvKAyh0O1lTUcyRHCSztPSOxMsgAK5eU04katjT0j/NTy0cp3tG+NYLLfxi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\nMJz0zMysMJz0zMysMJz0zMysMP4P26xojg0XXqQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7333bc588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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kXhiGMDObYHJa4XsKy5bQfYyMWSwtdBb+pDNG6IDpfqNSCdhYdalUFKmUMDph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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7337786a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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