PA_constrained_opt_student.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_star= [ 0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          1.1530358   0.          0.\n",
      "  0.         -1.74976547  0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.3426804   0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.        ]\n",
      "Non-zero coeffs= (array([21, 25, 51]),)\n",
      "Smoothness coeff= 1.9432632682679574\n"
     ]
    }
   ],
   "source": [
    "# Secret data generating mechanism that as the optimisation engineer you don't have access to. \n",
    "# However, to evaluate the final solution beyond the training objective \n",
    "# (which is quite likely close to zero for any training procedure due to huge number of parameters) \n",
    "# we need access to w_star. \n",
    "\n",
    "# You may feel free to use the variable data_dim. All other variables here are off limits. \n",
    "\n",
    "# Data description: 30 data points for 100 dimensional regression problem. \n",
    "\n",
    "data_dim = 100\n",
    "num_data = 30\n",
    "sparsity = 3\n",
    "np.random.seed(100) \n",
    "w_temp = np.random.randn(sparsity)\n",
    "indices = np.random.choice(data_dim, sparsity, replace=False)\n",
    "w_star=np.zeros(data_dim)\n",
    "w_star[indices]=w_temp\n",
    "\n",
    "data_matrix = np.random.randn(num_data, data_dim)*0.5\n",
    "labels = np.dot(data_matrix, w_star) + 0.0*np.random.randn(num_data)\n",
    "\n",
    "\n",
    "global_A = np.dot(data_matrix.T, data_matrix) / num_data\n",
    "global_b = np.dot(data_matrix.T,labels) / num_data\n",
    "global_c = 0.5* np.dot(labels, labels) / num_data\n",
    "global_w_star = np.array(w_star)\n",
    "\n",
    "print('w_star=', global_w_star)\n",
    "print('Non-zero coeffs=', np.where(np.abs(global_w_star)>1e-5))\n",
    "eig_vals, eig_vecs = np.linalg.eig(global_A)\n",
    "smoothness_coeff = np.real(np.max(eig_vals))\n",
    "print('Smoothness coeff=', smoothness_coeff)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eigenvalues of A\n",
    "\n",
    "The code in the cell below checks if the eigenvalues of A are negative. This would imply that the matrix A is not PSD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34 eigen values are negative\n"
     ]
    }
   ],
   "source": [
    "count = np.sum(eig_vals < 0)\n",
    "print(count, \"eigen values are negative\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def get_value(w):\n",
    "    A = global_A\n",
    "    b = global_b\n",
    "    return 0.5*np.dot(w, np.dot(A,w)) - np.dot(b,w) + global_c\n",
    "\n",
    "def get_gradient(w):\n",
    "    A = global_A\n",
    "    b = global_b\n",
    "    return np.dot(A,w)-b\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 1:\n",
    "\n",
    "Assume you have oracle access to a regression error function (call it f) on some training data. Solve the LASSO optimisation problem, over some given l1 norm ball using the projected gradient descent.\n",
    "\n",
    "1. Write the function for the l1 norm projection oracle, l2 norm projection oracle and the respective PGD steps.\n",
    "\n",
    "2. Plot f(w_t) vs t for the PGD algorithm with l2 norm projection oracle. The step size is fixed to eta=0.01. Repeat the plots with different l2 norm constraints: 0.1, 0.5, 1, 2, 5 (on the same plot). \n",
    "\n",
    "3. Plot f(w_t) vs t for the PGD algorithm with l1 norm projection oracle. The step size is fixed to eta=0.01. Repeat the plots with different l1 norm constraints: 0.1, 0.5, 1, 2, 5 (on the same plot).\n",
    "\n",
    "4. Let $w^1_\\lambda$ be the result of running PGD with the l1 norm constraint of lambda for 500 iterations. Similarly let $w^2_\\mu$ be the result of running PGD with the l2 norm constraint of mu for 500 iterations. Give two separate cells with each cell containing 2 plots as follows: \n",
    "\n",
    "    4a. In the first cell: $f(w^1_\\lambda)$ vs $\\lambda$ and $||w^1_\\lambda - w^* ||$ vs $\\lambda$.    \n",
    "    4b. In the Second cell: $f(w^2_\\mu)$ vs $\\mu$ and $||w^2_\\mu - w^* ||$ vs $\\mu$. \n",
    "    \n",
    "    Note 1: $w^*$ is the vector used in data generation. \n",
    "    Note 2: Using $w^*$ is illegal anywhere else. But it's okay here to just make a point.\n",
    "    Note 3: The range of mu and lambda to plot may be taken to be 0.1 to 3.\n",
    "    Note 4: We can take the norm above to simply be the difference in the set of non-zero components\n",
    "\n",
    "5. Summarise and explain your findings in a markdown cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Question 1 part 1\n",
    "\n",
    "def projection_oracle_l2(w, l2_norm):\n",
    "    \"\"\"Projects a given vector onto a ball (as defined by l2_norm) of given radius around the origin\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): given vector to be projected \n",
    "        l2_norm (ndarray): radius of the l2_norm ball\n",
    "    \n",
    "    Returns:\n",
    "        w_projected (ndarray): projected vector\n",
    "    \"\"\"\n",
    "    norm_w = np.sqrt(np.dot(w,w))\n",
    "    if norm_w <= l2_norm:\n",
    "        w_projected = w\n",
    "       \n",
    "    else:\n",
    "        w_hat = w/norm_w\n",
    "        w_projected = w_hat*l2_norm\n",
    "    \n",
    "    return w_projected\n",
    "\n",
    "def compute_l1_norm(x):\n",
    "    \"\"\"Function to compute the l1 norm of a given vector\n",
    "    \n",
    "    Args:\n",
    "        x (ndarray): vector whose l1 norm is to be computed\n",
    "    \n",
    "    Returns:\n",
    "        l1_norm (float): l1 norm of the given vector\n",
    "    \"\"\"\n",
    "    \n",
    "    x = np.array(x)\n",
    "    l1_norm = np.sum(np.abs(x))\n",
    "    \n",
    "    return l1_norm\n",
    "\n",
    "def vector_plus(x):\n",
    "    \"\"\"Function to retain positive values of a vector and set negative values to 0\n",
    "    \n",
    "    Args:\n",
    "        x (ndarray): input vector\n",
    "    \n",
    "    Returns:\n",
    "        x_plus (ndarray): output vector all of whose negative elements have been\n",
    "            set to zero\n",
    "    \"\"\"\n",
    "    x = np.array(x)\n",
    "    mask = x>0\n",
    "    x_plus = x*mask\n",
    "    \n",
    "    return x_plus\n",
    "\n",
    "\n",
    "def projection_oracle_l1(w, l1_norm):\n",
    "    \"\"\"Projects a given vector onto a ball (as defined by l1_norm) of given radius around the origin\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): given vector to be projected \n",
    "        l1_norm (ndarray): radius of the l1_norm ball about the origin\n",
    "    \n",
    "    Returns:\n",
    "        w_projected (ndarray): projected vector\n",
    "    \"\"\"\n",
    "    w = np.array(w)\n",
    "    w_sign = 2*(w>0) - 1\n",
    "    w_pos = np.abs(w)\n",
    "    w_norm = compute_l1_norm(w)\n",
    "    \n",
    "    if w_norm <= l1_norm:\n",
    "        w_projected = w\n",
    "    else:\n",
    "        # tolerance value in projection\n",
    "        epsilon = 10**(-5)\n",
    "        # original vector is outside l1 ball\n",
    "        tau_low = 0\n",
    "        \n",
    "        # finding a tau high that pushes given vector into l1 ball\n",
    "        tau_high = 1\n",
    "        one_vector = np.ones(len(w))\n",
    "        forced_vector = vector_plus(w_pos - tau_high*one_vector)\n",
    "        while compute_l1_norm(forced_vector) > l1_norm:\n",
    "            tau_high = 2*tau_high\n",
    "            forced_vector = vector_plus(w_pos - tau_high*one_vector)\n",
    "            \n",
    "        tau = (tau_high + tau_low)/2\n",
    "        w_projected = w_sign*vector_plus(w_pos - tau*one_vector) \n",
    "        norm_w_projected= compute_l1_norm(w_projected)\n",
    "        \n",
    "        while np.abs(norm_w_projected - l1_norm) > epsilon:\n",
    "            # \"projection\" too far in, gotta reduce tau\n",
    "            if norm_w_projected < l1_norm:\n",
    "                tau_high = tau\n",
    "            # \"projection\" is still too close to the original point\n",
    "            elif norm_w_projected > l1_norm:\n",
    "                tau_low = tau\n",
    "            tau = (tau_high + tau_low)/2\n",
    "            w_projected = w_sign*(vector_plus(w_pos - tau*one_vector))\n",
    "            norm_w_projected = compute_l1_norm(w_projected)\n",
    "    \n",
    "    return w_projected\n",
    "\n",
    "def PGD_step_l2(w, l2_norm, eta=0.1):\n",
    "    \"\"\"Performs one step of projected gradient descent for l2 norm\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): iterate at the t-th iteration\n",
    "        l2_norm (float): radius of the l2_norm ball onto which given vector must be projected\n",
    "        eta (float): step size for PGD\n",
    "    \n",
    "    Returns:\n",
    "        w_next_projected (ndarray): iterate at the t+1-th iteration\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    grad_w = get_gradient(w)\n",
    "\n",
    "    \n",
    "    # update\n",
    "    w_next = w - eta*grad_w\n",
    "    \n",
    "    # projection\n",
    "    w_next_projected = projection_oracle_l2(w_next, l2_norm)\n",
    "    \n",
    "    return w_next_projected\n",
    "\n",
    "def PGD_step_l1(w, l1_norm, eta=0.1):\n",
    "    \"\"\"Performs one step of projected gradient descent for l1 norm\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): iterate at the t-th iteration\n",
    "        l1_norm (float): radius of the l1_norm ball onto which given vector must be projected\n",
    "        eta (float): step size for PGD\n",
    "    \n",
    "    Returns:\n",
    "        w_next_projected (ndarray): iterate at the t+1-th iteration\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    grad_w = get_gradient(w)\n",
    "    \n",
    "    # update\n",
    "    w_next = w - eta*grad_w\n",
    "    \n",
    "    # projection\n",
    "    w_next_projected = projection_oracle_l1(w_next, l1_norm)\n",
    "    \n",
    "    return w_next_projected\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "norm constraint: 0.1 \n",
      " L2 norm of w: 0.09999999999999999 \n",
      " L1 norm of w 0.756876132752695\n",
      "norm constraint: 0.5 \n",
      " L2 norm of w: 0.5 \n",
      " L1 norm of w 3.698317302864997\n",
      "norm constraint: 1 \n",
      " L2 norm of w: 0.9999999999999999 \n",
      " L1 norm of w 7.268634616501321\n",
      "norm constraint: 2 \n",
      " L2 norm of w: 1.0488881049986283 \n",
      " L1 norm of w 7.62774105636881\n",
      "norm constraint: 5 \n",
      " L2 norm of w: 1.0488881049986283 \n",
      " L1 norm of w 7.62774105636881\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 part 2\n",
    "w_all = []\n",
    "f_vals_all=[]\n",
    "plt.figure()\n",
    "norm_constraint_vals = [0.1, 0.5, 1, 2, 5]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    f_vals=[]\n",
    "    w=np.zeros(data_dim)\n",
    "\n",
    "    for t in range(100):\n",
    "        w = PGD_step_l2(w, norm_constraint)\n",
    "        f_vals.append(get_value(w))\n",
    "        \n",
    "    print(\"norm constraint:\", norm_constraint,\"\\n\",\"L2 norm of w:\", \n",
    "          np.sqrt(np.dot(w,w)), \"\\n\", \"L1 norm of w\", compute_l1_norm(w))\n",
    "    w_all.append(w)\n",
    "    \n",
    "    \n",
    "    f_vals_all.append(f_vals)\n",
    "\n",
    "    \n",
    "################# Comparing solutions #####################\n",
    "# print(\"Energy of error between solutions obtained with 1,2,5 \")\n",
    "# print(np.sqrt(np.dot(w_all[-1] - w_all[-2],w_all[-1] - w_all[-2] )))\n",
    "# print(np.sqrt(np.dot(w_all[-1] - w_star,w_all[-1] - w_star )))\n",
    "# print(np.sqrt(np.dot(w_all[-2] - w_star,w_all[-2] - w_star )))\n",
    "\n",
    "# print(np.sqrt(np.dot(w_all[-3] - w_all[-2],w_all[-3] - w_all[-2] )))\n",
    "# print(np.sqrt(np.dot(w_all[-3] - w_star,w_all[-3] - w_star )))\n",
    "# print(np.sqrt(np.dot(get_gradient(w_all[-1]), get_gradient(w_all[-1]))))\n",
    "###########################################################\n",
    "\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(range(100),np.array(f_vals_all).T)\n",
    "plt.legend(norm_constraint_vals)\n",
    "plt.xlabel('Iteration: t')\n",
    "plt.ylabel('Loss : $f(x_t)$')\n",
    "plt.title('Loss vs Iteration for l2-norm ball PGD, with different l2 norm constraints')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 part 3\n",
    "\n",
    "f_vals_all=[]\n",
    "plt.figure()\n",
    "norm_constraint_vals = [0.1, 0.5, 1, 2, 5]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    f_vals=[]\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = PGD_step_l1(w, norm_constraint)\n",
    "        f_vals.append(get_value(w))\n",
    "    f_vals_all.append(f_vals)\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(range(100),np.array(f_vals_all).T)\n",
    "plt.legend(norm_constraint_vals)\n",
    "plt.xlabel('Iteration: t')\n",
    "plt.ylabel('Loss : $f(x_t)$')\n",
    "plt.title('Loss vs Iteration for l1-norm ball PGD, with different l1 norm constraints')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 part 4a\n",
    "\n",
    "norm_constraint_vals = np.arange(0.1,3,0.1)\n",
    "loss_values=[]\n",
    "deviation_from_truth=[]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = PGD_step_l2(w, norm_constraint)\n",
    "    loss_values.append(get_value(w))\n",
    "\n",
    "    # One measure of deviation is to check the non-zero components that are \n",
    "    # different in w and w_star\n",
    "    \n",
    "    nonzero_w_star = set(np.where(np.abs(global_w_star)>1e-5)[0])\n",
    "    nonzero_w = set(np.where(np.abs(w)>1e-5)[0])\n",
    "    deviation_from_truth.append( len(nonzero_w.symmetric_difference(nonzero_w_star)) )\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, loss_values)\n",
    "plt.xlabel('l2 norm constraint')\n",
    "plt.ylabel('Loss value at convergence')\n",
    "plt.title('L2 norm projected gradient descent')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, deviation_from_truth)\n",
    "plt.xlabel('l2 norm constraint')\n",
    "plt.ylabel('Deviation of learned $w$ from $w^*$')\n",
    "plt.title('L2 norm projected gradient descent')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 1 part 4b\n",
    "\n",
    "norm_constraint_vals = np.arange(0.1,3,0.1)\n",
    "loss_values=[]\n",
    "deviation_from_truth=[]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = PGD_step_l1(w, norm_constraint)\n",
    "    loss_values.append(get_value(w))\n",
    "    \n",
    "    # One measure of deviation is to check the non-zero components that are \n",
    "    # different in w and w_star\n",
    "    \n",
    "    nonzero_w_star = set(np.where(np.abs(global_w_star)>1e-5)[0])\n",
    "    nonzero_w = set(np.where(np.abs(w)>1e-5)[0])\n",
    "    deviation_from_truth.append( len(nonzero_w.symmetric_difference(nonzero_w_star)) )\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, loss_values)\n",
    "plt.xlabel('l1 norm constraint')\n",
    "plt.ylabel('Loss value at convergence')\n",
    "plt.title('L1 norm projected gradient descent')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, deviation_from_truth)\n",
    "plt.xlabel('l1 norm constraint')\n",
    "plt.ylabel('Deviation of learned $w$ from $w^*$')\n",
    "plt.title('L1 norm projected gradient descent')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l1_norm: 3.2454816789458434\n",
      "l2_norm: 2.1233465641558884\n"
     ]
    }
   ],
   "source": [
    "print(\"l1_norm:\", compute_l1_norm(w_star))\n",
    "print(\"l2_norm:\", (np.sqrt(np.dot(w_star, w_star))))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1 Part 5:\n",
    "\n",
    "**Note**: An implementation detail is that the same vector w_star is produced for every run of the notebook as the numpy random seed is set to a fixed value. Therefore, all analysis is presented for the w_star with\n",
    "\n",
    "- l1_norm(w*) = 3.24\n",
    "- l2_norm(w*) = 2.12\n",
    "\n",
    "#### Observations about L2 norm ball PGD:\n",
    "\n",
    "- The iterate and consequently the funciton value change very little for an l2 norm ball constraint of 0.1. However for radii of 0.5, 1, 2 and 5, the function value decreases for a few iterations and remains constant later on.\n",
    "- For L2 norm radius of 1,2 and 5 the solution converges to nearly the same point which is not equal to w_star. \n",
    "- In the first case, when radius = 0.1, the behaviour of PGD indicates that the chosen constraint is too small to make any progress. At every iteration, PGD is pushing $x_t$ out of the L2 norm ball which is then being projected back onto the same position leading to $x_t$ and $f(x_t)$ being nearly the same for every iteration. When the radius is 0.5, the algorithm makes some progress before the same process repeats. This can be numerically verified. Computation of the gradient after 100 iterations reveals that it is still non-zero (*code commented out in the cell*) indicating that the function can still be decreased. Further for radius = 0.1, 0.5 and 1, the solutions are all on the boundary.\n",
    "- In the case of radius = 2,5 the algorithm converges to a point inside the L2 norm ball after a 100 iterations which is not equal to w*. However, the evaluation of the gradient at this point reveals that it is quite close to zero $\\left( \\approx 10^{-3} \\right)$. This indicates that the function is converging to some local optimum and not necessarily w_star. \n",
    "\n",
    "Why is this possible? Consider the problem statement.\n",
    "\n",
    "\\begin{align}\n",
    "num\\_data &= 30 \\\\\n",
    "D &= data\\_matrix \\\\\n",
    "l &= labels = Dw^* \\\\\n",
    "A &= \\frac{D^TD}{30} \\\\\n",
    "B &= \\frac{D^Tl}{30} = \\frac{(D^TD)w^* }{30} \\\\\n",
    "C &= \\frac{l^Tl}{60} = \\frac{w^{* T}(D^T D) w^* }{60} \\\\\n",
    "f(w) &= \\frac{1}{2}w^T A W - B^Tw + C \\\\\n",
    "    &= \\frac{1}{60} w^T (D^T D) w - \\frac{1}{30} w^{* T} D^T D w + \\frac{1}{60} w^{* T} D^T D w^*  \n",
    "\\end{align}\n",
    "\n",
    "Clearly \n",
    "\n",
    "\\begin{equation}\n",
    "f(w^* ) = 0\n",
    "\\end{equation}\n",
    "\n",
    "Also\n",
    "\n",
    "\\begin{align}\n",
    "\\nabla f(w) &= \\frac{1}{30} (D^T D) w - \\frac{1}{30} (D^T D) w^* \\\\\n",
    "\\nabla f(w^* ) &= 0\n",
    "\\end{align}\n",
    "\n",
    "Clearly, if this were an unconstrained optimization problem, $w^*$ satisfies the FONC. Further f(w) is a quadratic in w. Therefore f(w) is convex **iff** $D^T D$ is PSD. However as shown at the start of the notebook this not true as A has negative eigenvalues. Therefore f(w) is non-convex and can have local optima. In this case there exists a stationary point with L2 norm $\\approx 1.04$ which the solution converges to. This is the solution that PGD with L2 norm ball radius = 1,2,5 converges to.\n",
    "\n",
    "#### Observations from L1 norm ball PGD:\n",
    "\n",
    "- PGD reaches lower values of the objective function for higher values of L1 norm ball radius. This can again be attributed to the radius of the ball being too small or sufficiently large as has been done above. \n",
    "- One interesting question to answer is why PGD with L1 norm ball radii 1,2 and 5 don't converge to the same solution (local optimum other than w^* ) as has been argued above. This is because the solution with L2 norm $\\approx 1.04$ has a L1 norm $> 7$ which is why it is not a feasible solution for the given problem.\n",
    "\n",
    "\n",
    "\n",
    "#### Observations from question 4:\n",
    "\n",
    "- Once again from the first plot of 4a it can be seen that for all values of the L2 norm constraint greater than one the algorithm converges to the same (not $w^*$) solution with f(w) = 0.\n",
    "- By comparing the plots of deviation of w from w_star it is evident that the deviation is lower in the case of    L1 norm projected gradient descent rather than L2 norm gradient descent. This is because the metric used to measure deviation is **\"the number of different non-zero components\"**. Firstly, this metric is appropriate as the w_star vector is chosen to be very sparse. L2 norm minimisation produces \"low energy\" solutions that is solutions with lower values of L2 norm but not necessarily sparse solutions. This is exactly what can be observed from the second curve of Question 1 part 4a. The solution obtained by the L2 norm projected gradient descent nearly always has a deviation of 97 as almost all of the 100 elements of w have some (small but) non-zero value.\n",
    "- In contrast, PGD constrained to the L1 norm ball produces sparse solutions. While the solutions produced do not necessarily equal w_star (as the L1 norm ball radius might not be large enough to include w_star), the number of unequal non-zero values is much lower as the solutions are more sparse.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2:\n",
    "\n",
    "Assume you have oracle access to a regression error function (call it f) on some training data. Solve the LASSO optimisation problem, over some given l1 norm ball using the Frank-Wolfe method. \n",
    "\n",
    "1. Write the function for the l1 norm LMO, l2 norm LMO and the respective FW steps.\n",
    "\n",
    "2. Plot f(w_t) vs t for the FW algorithm with l2 norm LMO. Repeat the plots with different l2 norm constraints: 0.1,0.5,1,2,5 (on the same plot). \n",
    "\n",
    "3. Plot f(w_t) vs t for the FW algorithm with l1 norm LMO. Repeat the plots with different l1 norm constraints: 0.1,0.5,1,2,5 (on the same plot). \n",
    "\n",
    "4. Let $w^1_\\lambda$ be the result of running FW with the l1 norm constraint of lambda for 500 iterations. Similarly let $w^2_\\mu$ be the result of running FW with the l2 norm constraint of mu for 500 iterations. Give two separate plots with each plot containing 2 curves as follows: \n",
    "\n",
    "    4a. In the first plot: $f(w^1_\\lambda)$ vs $\\lambda$ and $||w^1_\\lambda - w^* ||$ vs $\\lambda$.    \n",
    "    4b. In the Second plot: $f(w^2_\\mu)$ vs $\\mu$ and $||w^2_\\mu - w^* ||$ vs $\\mu$. \n",
    "    \n",
    "    Note 1: $w^*$ is the vector used in data generation. \n",
    "    Note 2: Using $w^*$ is illegal anywhere else. But it's okay here to just make a point.\n",
    "    Note 3: The range of mu and lambda to plot may be taken to be 0.1 to 3.\n",
    "    Note 4: We can take the norm above to simply be the difference in the set of non-zero components\n",
    "    \n",
    "5. Summarise and explain your findings on 2,3,4 above in a markdown cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Question 2 part 1\n",
    "\n",
    "\n",
    "def LMO_l2(u, l2_norm):\n",
    "    \"\"\"Linear minimization oracle for l2 norm ball\n",
    "    \n",
    "    Function to find the vector x belonging to the l2 norm ball\n",
    "    of radius l2_norm which minimizes u*x\n",
    "    \n",
    "    Args:\n",
    "        u (ndarray): direction of minimization\n",
    "        l2_norm (ndarray): radius of l2_norm ball\n",
    "    \n",
    "    Returns:\n",
    "        x (ndarray): vector belonging to the l2_norm ball which\n",
    "            minimizes u*x (dot product)\n",
    "    \"\"\"\n",
    "    u_norm = np.sqrt(np.dot(u,u))\n",
    "    x = l2_norm*(-1*u)/u_norm\n",
    "    \n",
    "    return x\n",
    "\n",
    "def LMO_l1(u, l1_norm):\n",
    "    \"\"\"Linear minimization oracle for l1 norm ball\n",
    "    \n",
    "    Function to find the vector x belonging to the l1 norm ball\n",
    "    of radius l1_norm which minimizes u*x. This amounts to testing \n",
    "    the vertices of the corner region of the l1 norm ball which is a \n",
    "    convex hull of hte vertex vectors.\n",
    "    \n",
    "    Args:\n",
    "        u (ndarray): direction of minimization\n",
    "        l1_norm (ndarray): radius of l1_norm ball\n",
    "    \n",
    "    Returns:\n",
    "        x (ndarray): vector belonging to the l1_norm ball which\n",
    "            minimizes u*x (dot product)\n",
    "    \"\"\"\n",
    "    \n",
    "    # vertices are simply +l1_norm*canonical_basis and -l1_norm*canonical_basis\n",
    "    num_dim = len(u)\n",
    "    vertices = l1_norm*np.concatenate((np.identity(num_dim), -1*np.identity(num_dim)), axis = 0)\n",
    "    dot_products = np.dot(vertices, u)\n",
    "    x = vertices[np.argmin(dot_products),:]\n",
    "    \n",
    "    return x\n",
    "    \n",
    "def FW_step_l2(w, l2_norm, gamma):\n",
    "    \"\"\"Function to perform one iteration of Frank-Wolfe for l2 norm ball constraint\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): iterate at the t-th iteration\n",
    "        l2_norm (float): radius of the l2_norm ball\n",
    "        gamma (float): parameter of the FW update\n",
    "        \n",
    "    Returns:\n",
    "        w_next (ndarray): iterate at the t+1-th iteration\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    grad_w = get_gradient(w)\n",
    "    y_t = LMO_l2(grad_w,l2_norm)\n",
    "    \n",
    "    w_next = gamma*y_t + (1 - gamma)*w\n",
    "    \n",
    "    return w_next\n",
    "    \n",
    "\n",
    "def FW_step_l1(w, l1_norm, gamma):\n",
    "    \"\"\"Function to perform one iteration of Frank-Wolfe for l1 norm ball constraint\n",
    "    \n",
    "    Args:\n",
    "        w (ndarray): iterate at the t-th iteration\n",
    "        l1_norm (float): radius of the l1_norm ball\n",
    "        gamma (float): parameter of the FW update\n",
    "        \n",
    "    Returns:\n",
    "        w_next (ndarray): iterate at the t+1-th iteration\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    grad_w = get_gradient(w)\n",
    "    y_t = LMO_l1(grad_w,l1_norm)\n",
    "    \n",
    "    w_next = gamma*y_t + (1 - gamma)*w\n",
    "    \n",
    "    return w_next\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 2 part 2\n",
    "\n",
    "f_vals_all=[]\n",
    "plt.figure()\n",
    "norm_constraint_vals = [0.1, 0.5, 1, 2, 5]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    f_vals=[]\n",
    "    w=np.zeros(data_dim)\n",
    "\n",
    "    for t in range(100):\n",
    "        w = FW_step_l2(w, norm_constraint, gamma=2./(t+2))\n",
    "        f_vals.append(get_value(w))\n",
    "    f_vals_all.append(f_vals)\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(range(100),np.array(f_vals_all).T)\n",
    "plt.legend(norm_constraint_vals)\n",
    "plt.xlabel('Iteration: t')\n",
    "plt.ylabel('Loss : $f(x_t)$')\n",
    "plt.title('Loss vs Iteration for l2-norm ball FW, with different l2 norm constraints')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 2 part 3\n",
    "\n",
    "f_vals_all=[]\n",
    "plt.figure()\n",
    "norm_constraint_vals = [0.1, 0.5, 1, 2, 5]\n",
    "\n",
    "# for value in list: does this not iterate through elements randomly\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "#     print(norm_constraint)\n",
    "    f_vals=[]\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = FW_step_l1(w, norm_constraint, gamma=2./(t+2))\n",
    "        f_vals.append(get_value(w))\n",
    "    f_vals_all.append(f_vals)\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(range(100),np.array(f_vals_all).T)\n",
    "plt.legend(norm_constraint_vals)\n",
    "plt.xlabel('Iteration: t')\n",
    "plt.ylabel('Loss : $f(x_t)$')\n",
    "plt.title('Loss vs Iteration for l1-norm ball FW, with different l1 norm constraints')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SpBEZNqBtDVwOvA44jcH8mN8ddVGSJEnTbNipnn4MnAd8CbgFOAm4edRFSZIkTbNh96AtB74FPILBlEwnVtXJI69KkiRpig0V0Krqoqo6Ang+8FDgnCSvGktlkiRJU2qoQ5xJZoAlwH0ZTPd0L/Bc4ISRVyZJkjSlhj0H7XDgJwwmLl//LOuSJEka2rBTPX1vTHVIkiSp41RPkiRJjTGgSZIkNcaAJkmS1JgFnYOW5L+va3lVvWU05UiSJGmhFwncv3v+dWBf4Izu/dOBc0ZdlCRJ0jRbUECrqtcBJPks8KiquqV7/1rgo2OrTpIkaQoNew7arsBds97fBSwbWTWSJEka+ka1HwS+kuR0oIBnAR8YeVWSJElTbNgb1b4hyZnAgd3QEVV18ejLkiRJml5DHeJMEuDhwNZV9XfAj5PsN5bKJEmSptSw56C9A9gfOLR7fwvw9pFWJEmSNOWGPQft0VX1qCQXA1TVjUm2HENdkiRJU2vYPWh3J9mMwQUCJNkBuHfkVUmSJE2xYQPaicDpwI5J3gB8EThh5FVJkiRNsWGv4jwlySrgICDAIVX1jbFUJkmSNKWGPQeNqroSuHIMtUiSJIkhA1qS+wDPYTB7wM8+W1WvH21ZkiRJ02vYPWifAG4CVgF3jr4cSZIkDRvQdq6qg8dSiSRJkoDhr+L8cpJHjKUSSZIkAcPvQTsAODzJdxkc4gxQVbXnyCuTJEmaUgsOaN08nC8BrhpfOZIkSVpwQKuqSvLWqtpnnAVJkiRNu2EPcZ6fZN+q+upYqmnc6z55OVdcc/Oky2jeT35yO+/85nmTLmPRs8/9sdf9sdf9sM/r9/AHPoDjn/6bE9v+sAFtJfAHSa4CbsVz0CRJkkZu2ID2lLFUsYmYZJLelMzMzLBixf6TLmPRs8/9sdf9sdf9sM/tG3YuzquSbAvsBmw1a5EXDkiSJI3IsFM9vRg4FtgZuAR4DHAe8MTRlyZJkjSdhr1R7bHAvsBVVbUSeCRw/cirkiRJmmLDBrQ7quoOGEycXlVXAr8++rIkSZKm17AXCVydZBvg48BZSW4Erhl9WZIkSdNr2IsEntW9fG2SLwBbA58ZeVWSJElTbKhDnBl4QZLXVNXZDC4U2Hs8pUmSJE2nYc9BewewP3Bo9/4W4O0jrUiSJGnKDXsO2qOr6lFJLgaoqhuTbDmGuiRJkqbWsHvQ7k6yGVAASXYA7h15VZIkSVNs2IB2InA6sGOSNwBfBE4YeVWSJElTbNirOE9Jsgo4iMFE6YdU1TfGUpkkSdKUGvYcNLqb0145hlokSZLEAgNaklvozjubuwioqnrASKuSJEmaYgsKaFV1/3EXIkmSpIFhLxKQJEnSmBnQJEmSGrOggJbkg93zseMtR5IkSQvdg7ZPkgcDv59k2yS/MvsxzgIlSZKmzUJvs/Eu4DPAQ4BVDK7eXKO6cUmSJI3AgvagVdWJVbU7cHJVPaSqfnXWw3AmSZI0QsPOJPDSJHsBB3ZD51TVpaMvS5IkaXoNdRVnkj8CTgF27B6nJHn5OAqTJEmaVsNO9fRi4NFVdStAkjcB5wFvG3VhkiRJ02rY+6AF+Oms9z/lFy8YkCRJ0kYadg/ae4ELkpzevT8EeM9oS5IkSZpuw14k8JYkM8ABDPacHVFVF4+jMEmSpGk17B40quoi4KIx1CJJkiSci1OSJKk5BjRJkqTGGNAkSZIaM9Q5aEnuAzwHWDb7s1X1+tGWJUmSNL2GvUjgE8BNDCZMv3P05UiSJGnYgLZzVR08lkokSZIEDH8O2peTPGIslUiSJAkYPqAdAKxK8s0klyb5epJLN7aIJMcmuSzJ5UmOmzX+8m5blyd588ZuR5IkaVMw7CHOp4y6gCR7AEcB+wF3AZ9J8ilgZ+CZwJ5VdWeSHUe9bUmSpBYNO9XTVUn2Ag7shs6tqq9tZA27A+dX1W0ASc4GngUsB95YVXd2275uI7cjSZK0SRjqEGeSY4FTgB27xz8meflG1nAZ8Pgk2yW5L/BUYBfgYcCBSS5IcnaSfTdyO5IkSZuEVNXCVx6cb7Z/Vd3avb8fcF5V7blRRSRHAscAq4ErgNuBJwP/ChwL7At8GHhIzSk4ydHA0QBLly7d59RTT513G6tXr2bJkiUbU6YWyF73wz73x173x173wz73Z129Xrly5aqqWj7fsmHPQQvw01nvf9qNbZSqeg/wHoAkJwBXMzj0+bEukH0lyb3A9sD1cz57EnASwPLly2vFihXzbmNmZoa1LdNo2et+2Of+2Ov+2Ot+2Of+bGivhw1o7wUuSHJ69/4QumC1MZLsWFXXJdkVeDawP3Av8ERgJsnDgC2BH23stiRJklo37EUCb+lO4n8cgz1nR1TVxSOo47Qk2wF3A8dU1Y1JTgZOTnIZg6s7D5t7eFOSJGkxGnYPGlW1isFUTyNTVQfOM3YX8IJRbkeSJGlTsKCAluSLVXVAkluA2XuxAlRVPWAs1UmSJE2hBQW0qjqge77/eMuRJEnSsPdBe9NCxiRJkrThhp2L88nzjI18+idJkqRpttBz0F4K/CHwkDmTo98f+PI4CpMkSZpWC72K8/8CZwJ/Bbxy1vgtVXXDyKuSJEmaYgu9SOAm4Cbg0CTbArsBWwEkoarOGV+JkiRJ02Wo+6AleTGDuTF3Bi4BHgOcx+CO/5IkSRqBYS8SWDNx+VVVtRJ4JHPmxpQkSdLGGTag3VFVdwAkuU9VXQn8+ujLkiRJml7DTvV0dZJtgI8DZyW5Ebhm9GVJkiRNr2EnS39W9/K1Sb4AbA18ZuRVSZIkTbGhJ0tfo6rOHmUhkiRJGnCydEmSpMY4WbokSVJjhp0s/RVJHjSuYiRJkjT8bTYeAHw2yblJjkmydBxFSZIkTbOhAlpVva6qfhM4BnggcHaSz42lMkmSpCk17B60Na4D/gP4MbDj6MqRJEnSsOegvTTJDPB5YHvgqKracxyFSZIkTath74P2YOC4qrpkHMVIkiRp+EOcrwL2SPK/AJLsmmS/0ZclSZI0vYYNaG8H9gd+r3t/SzcmSZKkERn2EOejq+pRSS4GqKobk2w5hrokSZKm1rB70O5OshnddE9JdgDuHXlVkiRJU2zYgHYicDqwNMkbgC8CJ4y8KkmSpCk21CHOqjolyfeBFQzugXZIVX1jHIVJkiRNqwUFtCQBjgdeBoTBnrd7gO2A14+tOkmSpCm00EOcxwGPA/atqu2qalvg0cDjkrxibNVJkiRNoYUGtBcBh1bVd9cMVNW/AS/olkmSJGlEFhrQtqiqH80drKrrgS1GW5IkSdJ0W2hAu2sDl0mSJGlIC72Kc68kN88zHmCrEdYjSZI09RYU0Kpqs3EXIkmSpIFhb1QrSZKkMTOgSZIkNcaAJkmS1BgDmiRJUmMMaJIkSY0xoEmSJDXGgCZJktQYA5okSVJjDGiSJEmNMaBJkiQ1xoAmSZLUGAOaJElSYwxokiRJjTGgSZIkNcaAJkmS1BgDmiRJUmMMaJIkSY0xoEmSJDXGgCZJktQYA5okSVJjDGiSJEmNMaBJkiQ1xoAmSZLUGAOaJElSYwxokiRJjTGgSZIkNcaAJkmS1BgDmiRJUmMMaJIkSY0xoEmSJDXGgCZJktQYA5okSVJjDGiSJEmNMaBJkiQ1xoAmSZLUGAOaJElSYwxokiRJjTGgSZIkNcaAJkmS1JgmAlqSY5NcluTyJMfNWfYnSSrJ9pOqT5IkqU8TD2hJ9gCOAvYD9gKelmS3btkuwJOBf59chZIkSf2aeEADdgfOr6rbquoe4GzgWd2ytwL/A6hJFSdJktS3FgLaZcDjk2yX5L7AU4FdkjwD+EFVfW2y5UmSJPUrVZPfOZXkSOAYYDVwBXA78Fjgv1bVTUm+Byyvqh/N89mjgaMBli5dus+pp5467zZWr17NkiVLxvMH6BfY637Y5/7Y6/7Y637Y5/6sq9crV65cVVXL51vWRECbLckJwA+BVwO3dcM7A9cA+1XVf6zts8uXL68LL7xw3mUzMzOsWLFitMVqXva6H/a5P/a6P/a6H/a5P+vqdZK1BrQWDnGSZMfueVfg2cAHqmrHqlpWVcuAq4FHrSucSZIkLRabT7qAzmlJtgPuBo6pqhsnXZAkSdKkNBHQqurA9Sxf1lMpkiRJE9fEIU5JkiT9nAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJaowBTZIkqTEGNEmSpMYY0CRJkhpjQJMkSWqMAU2SJKkxBjRJkqTGGNAkSZIa00RAS3JsksuSXJ7kuG7sr5NcmeTSJKcn2WbSdUqSJPVh4gEtyR7AUcB+wF7A05LsBpwF7FFVewLfAv58clVKkiT1Z+IBDdgdOL+qbquqe4CzgWdV1We79wDnAztPrEJJkqQetRDQLgMen2S7JPcFngrsMmed3wfO7L0ySZKkCUhVTboGkhwJHAOsBq4Abq+qV3TLXg0sB55d8xSb5GjgaIClS5fuc+qpp867jdWrV7NkyZLx/AH6Bfa6H/a5P/a6P/a6H/a5P+vq9cqVK1dV1fL5ljUR0GZLcgJwdVW9I8lhwEuAg6rqtvV9dvny5XXhhRfOu2xmZoYVK1aMtFbNz173wz73x173x173wz73Z129TrLWgLb5OItaqCQ7VtV1SXYFng3sn+Rg4M+AJywknEmSJC0WTQQ04LQk2wF3A8dU1Y1J/h64D3BWEhhcSPCSSRYpSZLUhyYCWlUdOM/YQydRiyRJ0qS1cBWnJEmSZjGgSZIkNcaAJkmS1BgDmiRJUmMMaJIkSY0xoEmSJDXGgCZJktQYA5okSVJjDGiSJEmNaW6y9I2R5HrgqrUs3h74UY/lTDN73Q/73B973R973Q/73J919frBVbXDfAsWVUBblyQXrm3GeI2Wve6Hfe6Pve6Pve6Hfe7PhvbaQ5ySJEmNMaBJkiQ1ZpoC2kmTLmCK2Ot+2Of+2Ov+2Ot+2Of+bFCvp+YcNEmSpE3FNO1BkyRJ2iQsuoCW5OAk30zynSSvnGf5fZJ8uFt+QZJl/Ve5OCyg14cnuT7JJd3jxZOoc1OX5OQk1yW5bC3Lk+TE7r/DpUke1XeNi8EC+rwiyU2zfs+v6bvGxSDJLkm+kOQbSS5Pcuw86/ibHoEF9trf9Qgk2SrJV5J8rev16+ZZZ6j8sagCWpLNgLcDTwEeDhya5OFzVjsSuLGqHgq8FXhTv1UuDgvsNcCHq2rv7vHuXotcPN4HHLyO5U8BduseRwPv7KGmxeh9rLvPAOfO+j2/voeaFqN7gD+uqt2BxwDHzPNvh7/p0VhIr8Hf9SjcCTyxqvYC9gYOTvKYOesMlT8WVUAD9gO+U1X/VlV3AacCz5yzzjOB93ev/wk4KEl6rHGxWEivNQJVdQ5wwzpWeSbwgRo4H9gmyU79VLd4LKDPGoGquraqLupe3wJ8A3jQnNX8TY/AAnutEeh+q6u7t1t0j7kn+Q+VPxZbQHsQ8P1Z76/mP/8Yf7ZOVd0D3ARs10t1i8tCeg3wnO4QxT8l2aWf0qbOQv9baOPt3x3CODPJb066mE1dd4jnkcAFcxb5mx6xdfQa/F2PRJLNklwCXAecVVVr/V0vJH8stoA2XxKdm2AXso7WbyF9/CSwrKr2BD7Hz//PQaPlbyICMtoAAAV6SURBVLofFzGYlmUv4G3AxydczyYtyRLgNOC4qrp57uJ5PuJvegOtp9f+rkekqn5aVXsDOwP7JdljzipD/a4XW0C7Gpi9l2Zn4Jq1rZNkc2BrPKyxIdbb66r6cVXd2b39B2CfnmqbNgv53WsjVdXNaw5hVNWngS2SbD/hsjZJSbZgEBhOqaqPzbOKv+kRWV+v/V2PXlX9BJjhP5/TOlT+WGwB7avAbkl+NcmWwO8CZ8xZ5wzgsO71c4F/LW8GtyHW2+s554w8g8H5Dxq9M4AXdVe+PQa4qaqunXRRi02S/7LmfJEk+zH49/PHk61q09P18D3AN6rqLWtZzd/0CCyk1/6uRyPJDkm26V7/MvAk4Mo5qw2VPzYfR6GTUlX3JHkZ8C/AZsDJVXV5ktcDF1bVGQx+rB9M8h0GyfV3J1fxpmuBvf6jJM9gcCXRDcDhEyt4E5bkQ8AKYPskVwPHMzgBlap6F/Bp4KnAd4DbgCMmU+mmbQF9fi7w0iT3ALcDv+v/3G2QxwEvBL7ena8D8CpgV/A3PWIL6bW/69HYCXh/d4eDXwI+UlX/vDH5w5kEJEmSGrPYDnFKkiRt8gxokiRJjTGgSZIkNcaAJkmS1BgDmiRJUmMMaJJ6lWR197x3kvOSXN5NB/a8SdfWh+7vfuoGfO6BSf5pAeu9asMqk9QSb7MhqVdJVlfVkiQPYzDH8LeTPBBYBeze3YV7VNvavJvzrhlJDgeWV9XL5lm20fWu6e/GfIekyXMPmqSJqKpvVdW3u9fXMJhgeIe56yWZSfKmJF9J8q0kB3bjWyV5b5KvJ7k4ycpu/PAkH03ySeCzSVYkOTvJR7rPvzHJ87vv+3qSX5tnm0tmffelSZ7TjR/ajV2W5E2z1l+d5A3dhNPnJ1najf92t+7XkpzTzbrxeuB5SS5J8rwkr01yUpLPAh9IsizJuUku6h6P7b5rWZLLZv2NH0vymSTfTvLmbvyNwC93333KyP5jSerdoppJQNKmqZtiZkvg/61llc2rar/u0ODxDKZROQagqh6R5DcYhLGHdevvD+xZVTckWQHsBezO4O7d/wa8u/u+Y4GXA8fN2d7/YjC90CO6+rbt9vK9icGcsjd22zukqj4O3A84v6pe3YWlo4C/BF4D/Leq+kGSbarqriSvYdYetCSv7b7zgKq6Pcl9gSdX1R1JdgM+BCyfpyd7A48E7gS+meRtVfXKJC/rJmyWtAlzD5qkicpgztYPAkdU1b1rWW3NJM+rgGXd6wO6z1FVVwJXAWsC2llVNXsS4q9W1bVVdSeDEPjZbvzrs75vticBb1/zpqpuBPYFZqrq+u4w5CnA47tV7gL+eZ4avwS8L8lRDKZEW5szqur27vUWwD8k+TrwUeDha/nM56vqpqq6A7gCePA6vl/SJsY9aJImJskDgE8B/7Oqzl/Hqnd2zz/l5/9uZR3r37qWzwPcO+v9vcz/72CAuSformt7d8+av/BnNVbVS5I8Gvgt4JIka9uzNbveVwA/ZLDX75eAO9bymdl/0+y+SFoE3IMmaSK687FOBz5QVR/dgK84B3h+910PYzAB9DdHVN5ngZ+dxJ9kW+AC4AlJtu8mRD4UOHtdX5Lk16rqgqp6DfAjYBfgFuD+6/jY1sC13d7EF7LuPW/zuTvJFkN+RlJjDGiSJuV3GBwiPLw7qX1de5jm8w5gs+5Q4IeBw7tDmKPwl8C2a07wB1ZW1bXAnwNfAL4GXFRVn1jP9/z1mosKGATKr3Wff/iaiwTW8ncdluR8Bods5+4NXJ+TgEu9SEDatHmbDUmSpMa4B02SJKkxBjRJkqTGGNAkSZIaY0CTJElqjAFNkiSpMQY0SZKkxhjQJEmSGmNAkyRJasz/B83RpUZyIYIxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 2 part 4a\n",
    "\n",
    "\n",
    "norm_constraint_vals = np.arange(0.1,3,0.1)\n",
    "loss_values=[]\n",
    "deviation_from_truth=[]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = FW_step_l2(w, norm_constraint, gamma=2./(t+2))\n",
    "    loss_values.append(get_value(w))\n",
    "\n",
    "    # One measure of deviation is to check the non-zero components that are \n",
    "    # different in w and w_star\n",
    "    \n",
    "    nonzero_w_star = set(np.where(np.abs(global_w_star)>1e-5)[0])\n",
    "    nonzero_w = set(np.where(np.abs(w)>1e-5)[0])\n",
    "    deviation_from_truth.append( len(nonzero_w.symmetric_difference(nonzero_w_star)) )\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, loss_values)\n",
    "plt.xlabel('l2 norm constraint')\n",
    "plt.ylabel('Loss value at convergence')\n",
    "plt.title('L2 norm FW')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, deviation_from_truth)\n",
    "plt.xlabel('l2 norm constraint')\n",
    "plt.ylabel('Deviation of learned $w$ from $w^*$')\n",
    "plt.title('L2 norm FW')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Question 2 part 4b\n",
    "\n",
    "\n",
    "norm_constraint_vals = np.arange(0.1,3,0.1)\n",
    "loss_values=[]\n",
    "deviation_from_truth=[]\n",
    "for norm_constraint in norm_constraint_vals:\n",
    "    w=np.zeros(data_dim)\n",
    "    for t in range(100):\n",
    "        w = FW_step_l1(w, norm_constraint, gamma=2./(t+2))\n",
    "    loss_values.append(get_value(w))\n",
    "    \n",
    "    # One measure of deviation is to check the non-zero components that are \n",
    "    # different in w and w_star\n",
    "    \n",
    "    nonzero_w_star = set(np.where(np.abs(global_w_star)>1e-5)[0])\n",
    "    nonzero_w = set(np.where(np.abs(w)>1e-5)[0])\n",
    "    deviation_from_truth.append( len(nonzero_w.symmetric_difference(nonzero_w_star)) )\n",
    "    \n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, loss_values)\n",
    "plt.xlabel('l1 norm constraint')\n",
    "plt.ylabel('Loss value at convergence')\n",
    "plt.title('L1 norm FW')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.grid()\n",
    "plt.plot(norm_constraint_vals, deviation_from_truth)\n",
    "plt.xlabel('l1 norm constraint')\n",
    "plt.ylabel('Deviation of learned $w$ from $w^*$')\n",
    "plt.title('L1 norm FW')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2 part 5\n",
    "\n",
    "- For the L2 norm ball, the LMO is implemented by finding that vector whose norm equals the radius of the ball and which is opposite to the direction of the gradient vector at $x_t$ i.e \n",
    "\\begin{equation}\n",
    "LMO(u,l2\\_norm) = l2\\_norm*\\frac{-u}{||u||}\n",
    "\\end{equation}\n",
    "\n",
    "- For FW (Frank-Wolfe) with L2 norm ball, loss approaches 0 for l2 norm ball radii of 1,2,5. Loss reaches a non-zero near constant value in 20 iterations for smaller radii. This is again because the radius is not large enough to include a region in which the algorithm can find an optimum value. \n",
    "\n",
    "- The results of part 2 reveal that there are \"oscillations\" in the loss value for the L2 norm constraints of 2 and 5. This shows that Frank Wolfe is not a descent algorithm i.e the function value is not guaranteed to decrease at every iteration.\n",
    "\n",
    "- For FW with the L1 norm ball the LMO is implemented by finding a vertex of the constraint region whose inner product with the desired (gradient) vector is minimum. From the curves obtained for part 3 it is seen that loss approaches zero after 20 iterations only for L1 norm radius = 5. This indicates that of all the tested values only this region encloses a potential optimum solution which the algorithm finds. Also, once again, the decrease in the loss function values is not monotonic.\n",
    "\n",
    "- Once again, from the second plots of question 4a and 4b it is evident that optimizing over the L1 norm ball produces sparse solutions which have a lower \"deviation\" (as defined) than do those produced by optimizing over the L2 norm ball. This is why the value of deviation for the L2 norm ball Frank Wolfe remains 97 throughout whereas the deviation in plot 2 of part 4b is very small.\n",
    "\n",
    "- The first plot of 4a indicates yet again that even the Frank Wolfe algorithm finds an optimum near one after which expanding the constraint region (increasing the radius of the ball) has no effect and the same optimum is discovered. In the case of 4b, plot 1 reveals that increasing the L1 norm ball radius expands the feasible region to allow better and better solutions closer the optimum.\n"
   ]
  }
 ],
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