Assignment_1_8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 8 LBFGS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import collections\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "verbosity = False\n",
    "# Utils\n",
    "\n",
    "def inverse_sigmoid(var):\n",
    "    '''\n",
    "    return 1/(1+exp(var))\n",
    "    avoid large overflow\n",
    "    '''\n",
    "    if var>=0:\n",
    "        return np.exp(-var)/(1+np.exp(-var))\n",
    "    else:\n",
    "        return 1/(1+np.exp(var))\n",
    "\n",
    "def init_weights(m):\n",
    "    '''\n",
    "    Generate random weights in [0,1]\n",
    "    '''\n",
    "    return np.random.rand(m, 1)\n",
    "\n",
    "def logistic_loss_vectorized(w, X, y, la):\n",
    "    '''\n",
    "    input: w parameter, X variables, y label, la lambda\n",
    "    Assignment 6.1\n",
    "    return f as the loss function value and g as the gradient\n",
    "    '''\n",
    "    x_mul_w = np.matmul(X, w)\n",
    "    y_X_w = np.multiply(y, x_mul_w)\n",
    "    f = np.sum(np.logaddexp(0, -y_X_w)) + la * np.sum(np.multiply(w,w))\n",
    "    inv_sigmoid_vector = np.exp(np.minimum(0, -y_X_w))/(1 + np.exp(np.multiply(-y_X_w,np.sign(y_X_w)))) # n * 1\n",
    "    y_inv_sigmoid = -1 * np.multiply(y, inv_sigmoid_vector)\n",
    "    g =  np.matmul(y_inv_sigmoid.reshape(1,-1),X) + 2 * la * w.reshape(1,-1)\n",
    "    g = g.reshape(-1, 1)\n",
    "    return (f, g)\n",
    "\n",
    "def hinge_loss_vectorized(w, X, y, la):\n",
    "    '''\n",
    "    input: w parameter, X variables, y label, la lambda\n",
    "    Assignment 6.2\n",
    "    return f as the loss function value and g as the gradient\n",
    "    '''\n",
    "    n = X.shape[0]\n",
    "    X_cdot_w = np.matmul(X, w)\n",
    "    one_minus = 1 - np.multiply(X_cdot_w, y)\n",
    "    f = np.sum(np.maximum(0, one_minus)) + la * np.sum(np.multiply(w,w))\n",
    "    minus_y = -1 * np.multiply(y, np.double(one_minus>0))\n",
    "    g = np.matmul(minus_y.reshape(1,-1),X).reshape(-1,1)  + 2 * la *w.reshape(-1,1)\n",
    "    g = g.reshape(-1,1)\n",
    "    return (f, g)\n",
    "\n",
    "# Load data\n",
    "'''\n",
    "Copied from https://github.com/rishabhk108/OptimizationML/tree/master/Assignments/data/README.md\n",
    "'''\n",
    "\n",
    "from scipy.io import loadmat\n",
    "import numpy as np\n",
    "def load_data():\n",
    "    X = loadmat(r\"train.mat\")\n",
    "    y = np.loadtxt(r\"train.targets\").reshape(-1, 1)\n",
    "    X = X['X'].todense()\n",
    "    # print(X.shape)\n",
    "    # print(y.shape)\n",
    "    return X,y\n",
    "\n",
    "def plot(losses, labels):\n",
    "    fig,ax = plt.subplots()\n",
    "    for i in range(len(losses)):\n",
    "        ax.plot(range(1,len(losses[i])+1), losses[i], label=labels[i])\n",
    "    ax.legend()\n",
    "    ax.set_xlabel(\"# Iterations\")\n",
    "    ax.set_ylabel(\"Loss Function Value\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### LBFGS ###\n",
      "## Logistic Loss ##\n",
      "### LBFGS ###\n",
      "## Hinge Loss ##\n",
      "### LBFGS ###\n",
      "## Logistic Loss ##\n",
      "### LBFGS ###\n",
      "## Hinge Loss ##\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def LBFGS_direction(g_k, S_ell, Y_ell, h):\n",
    "    '''\n",
    "    return the gradient descent direction of next step\n",
    "    s_k = w_{k+1} - w_k\n",
    "    y_k = g_{k+1} - g_k\n",
    "    p_k = 1/(y_k^T.s_k)\n",
    "    H_k = (B_k)^{-1} (inverse of B_k)\n",
    "    H_{k+1} = (I - s_k.y_k^T)/s_k^T.y_{k}) H_k (I - y_k.s_k^T)/y_k^T.s_k) + s_k.s_k^T/y_k^T.s_k\n",
    "            = (I - p_k.s_k.y_k^T}) H_k (I - p_k.y_k.s_k^T) + p_k.s_k.s_k^T\n",
    "    Assuming H_{k}=I\n",
    "    q_k = g_k\n",
    "    q_i = (I - p_i.y_i.s_i^T) * q_{i+1}\n",
    "    a_i = p_i.s_i^T * q_{i+1}\n",
    "    then q_i = q_{i+1} - a_i.y_i\n",
    "    beta_i = p_i.y_i^T.z_i\n",
    "    z_i = H_i.q_i\n",
    "    '''\n",
    "    q = g_k\n",
    "    p = np.zeros(len(S_ell))\n",
    "    a = np.zeros(len(S_ell))\n",
    "    Q1 = g_k\n",
    "    for i in range(len(S_ell)-1, -1, -1):\n",
    "        p[i] = 1/np.dot(Y_ell[i].T, S_ell[i])[0,0] # p_i = 1/(y_i^T.s_i) # ro ?\n",
    "        a[i] = p[i] * np.dot(S_ell[i].T, q)[0,0] # a_i = p_i.s_i^T * q_{i+1}\n",
    "        if i == 0:\n",
    "            Q1 = q\n",
    "        q = q - a[i] * Y_ell[i] # q_i = q_{i+1} - a_i.y_i\n",
    "    # gamma_k = s_{k-1}^T.y_{k-1}/ y_{k-1}^T.y_{k-1} # approximation\n",
    "    # gamma_k = np.dot(S_ell[-1].T, Y_ell[-1])[0,0]/np.dot(Y_ell[-1].T, Y_ell[-1])[0,0]\n",
    "    # H_{k-l} = gamma_k * I\n",
    "    # H_k_0 = gamma_k * np.identity(q.shape[0])\n",
    "    z = h * Q1\n",
    "    for i in range(len(S_ell)):\n",
    "        beta_i = p[i] * np.dot(Y_ell[i].T, z)[0,0] \n",
    "        z = z + S_ell[i] * (a[i]-beta_i) # z_{i+1} = z_i + (a_i - beta_i)s_i\n",
    "    return -z # alpha * -z = s_k\n",
    "\n",
    "def LBFGS(func_obj, w, max_iter, alpha, X, y, la, gamma, ell):\n",
    "    f, g = func_obj(w, X, y, la)\n",
    "    S_ell = collections.deque()\n",
    "    Y_ell = collections.deque()\n",
    "    # alpha = alpha / LA.norm(g, 1) # initialize of alpha\n",
    "    z = -g\n",
    "    pre_w = w\n",
    "    pre_f = f\n",
    "    pre_g = g\n",
    "    loss = [f, ]\n",
    "    for cur_iter in range(1, max_iter+1):\n",
    "        w_tent = w + alpha * z\n",
    "        f_tent, g_tent = func_obj(w_tent, X, y, la)\n",
    "        s_k = w_tent - w\n",
    "        y_k = g_tent - g\n",
    "        S_ell.append(s_k)\n",
    "        Y_ell.append(y_k)\n",
    "        if len(S_ell)>ell:\n",
    "            S_ell.popleft()\n",
    "            Y_ell.popleft()\n",
    "        h = alpha*(np.dot(z.T, Y_ell[-1])[0,0])/(np.dot(Y_ell[-1].T, Y_ell[-1])[0,0]);\n",
    "        z = LBFGS_direction(g_tent, S_ell, Y_ell, h)\n",
    "        if verbosity:\n",
    "            print(\"Iteration: \" + str(cur_iter) + \", alpha = \" + str(alpha) +\n",
    "              \", Loss Function Value = \" + str(f_tent))\n",
    "        pre_f = f\n",
    "        pre_g = g\n",
    "        w = w_tent\n",
    "        g = g_tent\n",
    "        f = f_tent\n",
    "        loss.append(f)\n",
    "    return loss\n",
    "\n",
    "def LBFGS_line_search(func_obj, w, max_iter, alpha, X, y, la, gamma, ell):\n",
    "    # verbosity=True\n",
    "    x = w # x\n",
    "    f, g = func_obj(x, X, y, la)\n",
    "    S_ell = collections.deque()\n",
    "    Y_ell = collections.deque()\n",
    "    loss = [f,]\n",
    "    alpha = alpha / LA.norm(g, 1) # initialize of alpha\n",
    "    z = -g\n",
    "    cur_iter = 1\n",
    "    while cur_iter<=max_iter:\n",
    "        x_tent = x + alpha * z\n",
    "        f_tent, g_tent = func_obj(x_tent, X, y, la)\n",
    "        gd = np.dot(g.T, -z)[0,0]\n",
    "        cur_iter += 1\n",
    "        backtracking = False\n",
    "        while f_tent > f - alpha * gamma* gd: # Armijo condition f(w-ag) \\le f(w) - alpha * gamma * ||g||^2\n",
    "            alpha = alpha*alpha*gd /(2*(f_tent + alpha* gd - f))  # Armijo v3 interpolation\n",
    "            x_tent = x + alpha * z\n",
    "            loss.append(f)\n",
    "            f_tent, g_tent = func_obj(x_tent, X, y, la)\n",
    "            cur_iter += 1\n",
    "            backtracking = True\n",
    "        s_k = x_tent - x\n",
    "        y_k = g_tent - g\n",
    "        S_ell.append(s_k)\n",
    "        Y_ell.append(y_k)\n",
    "        if len(S_ell)>ell:\n",
    "            S_ell.popleft()\n",
    "            Y_ell.popleft()\n",
    "        if verbosity:\n",
    "            print(\"Iteration: \" + str(cur_iter) + \", alpha = \" + str(alpha) +\n",
    "              \", Loss Function Value = \" + str(f_tent))\n",
    "        h = alpha*(np.dot(z.T, Y_ell[-1])[0,0])/(np.dot(Y_ell[-1].T, Y_ell[-1])[0,0]);\n",
    "        x = x_tent\n",
    "        g = g_tent\n",
    "        f = f_tent\n",
    "        z = LBFGS_direction(g_tent, S_ell, Y_ell, h)\n",
    "        if backtracking:\n",
    "            loss.append(f)\n",
    "        alpha = 1\n",
    "    return loss\n",
    "\n",
    "def test_LBFGS(ell):\n",
    "    '''\n",
    "    ell is how many previous step we store\n",
    "    '''\n",
    "    X,y = load_data()\n",
    "    w = init_weights(X.shape[1])\n",
    "    print('''### LBFGS ###''')\n",
    "    print('''## Logistic Loss ##''')\n",
    "    logistic_loss = LBFGS(logistic_loss_vectorized, w, 250, 1e-05, X, y, 1.0, 0.0001, ell)\n",
    "    print('''### LBFGS ###''')\n",
    "    print('''## Hinge Loss ##''')\n",
    "    hinge_loss = LBFGS(hinge_loss_vectorized, w, 250, 1e-05, X, y, 1.0, 0.0001, ell)\n",
    "    plot([logistic_loss,],['''Logistic Loss LBFGS ell='''+str(ell),])\n",
    "    plot([hinge_loss,],['''Hinge Loss LBFGS ell='''+str(ell),])\n",
    "    return [logistic_loss, hinge_loss], '''LBFGS ell30'''+str(ell)\n",
    "    \n",
    "def test_LBFGS_line_search(ell):\n",
    "    '''\n",
    "    ell is how many previous step we store\n",
    "    '''\n",
    "    X,y = load_data()\n",
    "    w = init_weights(X.shape[1])\n",
    "    print('''### LBFGS ###''')\n",
    "    print('''## Logistic Loss ##''')\n",
    "    logistic_loss = LBFGS_line_search(logistic_loss_vectorized, w, 250, 1, X, y, 1.0, 0.0001, ell)\n",
    "    print('''### LBFGS ###''')\n",
    "    print('''## Hinge Loss ##''')\n",
    "    hinge_loss = LBFGS_line_search(hinge_loss_vectorized, w, 250, 1, X, y, 1.0, 0.0001, ell)\n",
    "    plot([logistic_loss,],['''Logistic Loss LBFGS line search ell='''+str(ell),])\n",
    "    plot([hinge_loss,],['''Hinge Loss LBFGS line search ell='''+str(ell),])\n",
    "    return [logistic_loss, hinge_loss], '''LBFGS ell30'''+str(ell)\n",
    "\n",
    "func6_res, func6_label = test_LBFGS(20)\n",
    "func6_res_mod, func6_label_mod = test_LBFGS_line_search(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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