a1a.ipynb

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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/bin/bash: wget: command not found\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.signal import savgol_filter\n",
    "from sklearn.datasets import load_svmlight_file\n",
    "from method import SGD,SPS,SPSlack\n",
    "\n",
    "import sys\n",
    "import math\n",
    "import seaborn as sns\n",
    "import random\n",
    "from tqdm import tqdm\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "markers = [\"v\",\"^\",\"<\",\">\",\"o\",\"s\",\"p\",\"P\",\"*\"]\n",
    "colors = sns.color_palette(\"colorblind\")\n",
    "!wget https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/binary/a1a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1605, 119)\n"
     ]
    }
   ],
   "source": [
    "from joblib import Memory\n",
    "from sklearn.datasets import load_svmlight_file\n",
    "mem=Memory(\"./mecache\")\n",
    "def get_data(filePath):\n",
    "    data = load_svmlight_file(filePath)\n",
    "    return data[0], data[1]\n",
    "\n",
    "A, y = get_data(\"a1a\")\n",
    "lambd=0.01\n",
    "A = A.todense()\n",
    "A = np.array(A)\n",
    "\n",
    "n = A.shape[0]\n",
    "d = A.shape[1]\n",
    "print(A.shape,y.shape)\n",
    "\n",
    "#initialization\n",
    "np.random.seed(10)\n",
    "x0=0.1*np.random.randn(d,) #starting position\n",
    "s0=0.1\n",
    "def cost(x, random_ind):\n",
    "    batch_size = len(random_ind)\n",
    "    f = np.sum(np.log(1+np.exp(-np.dot(A[random_ind], x) * y[random_ind])))/(2*batch_size)\n",
    "    return f\n",
    "\n",
    "def grad(x, random_ind):\n",
    "    batch_size = len(random_ind)\n",
    "    num = -y[random_ind]\n",
    "    den = (1 + np.exp(np.dot(A[random_ind], x) * y[random_ind]))\n",
    "    c = num/den\n",
    "    c2 = np.dot(c.T,A[random_ind])\n",
    "    final_grad = (c2)/(2*batch_size) \n",
    "    return final_grad\n",
    "\n",
    "def hess(x):\n",
    "    hess_res = lambd*np.identity(d)\n",
    "    for i in range(n):\n",
    "        update_hess = (0.5/n) * (y[i]**2) * (np.exp(y[i]*np.dot(A[i],x))) * np.outer(A[i],A[i]) / (1+np.exp(y[i]*np.dot(A[i],x)))**2\n",
    "        hess_res = hess_res + update_hess\n",
    "    eigs,_ = la.eig(hess_res)\n",
    "    return np.min(eigs),np.max(eigs)\n",
    "    \n",
    "f0=cost(x0,range(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SGD\n",
    "#full batch\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "gamma = 1\n",
    "_,ff_star,_ = SGD(cost, grad, hess, K, gamma, x0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SGD')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=2,label = 'SGD', markevery=2000)\n",
    "plt.legend(fontsize=12)\n",
    "plt.title(r\"Toy Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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307.79412 154.986471 \nL 308.065306 213.784096 \nL 308.334833 213.695016 \nL 308.868992 165.228112 \nL 309.133662 202.179349 \nL 309.396753 104.121739 \nL 309.658282 212.843388 \nL 309.918268 218.954346 \nL 310.176729 123.407659 \nL 310.433684 214.430331 \nL 310.689148 187.531725 \nL 310.943141 208.574199 \nL 311.195677 219.713827 \nL 311.69645 134.893367 \nL 311.944719 211.29991 \nL 312.191596 130.704917 \nL 312.437098 220.60943 \nL 312.68124 191.414166 \nL 312.924037 179.834287 \nL 313.165504 190.107212 \nL 313.405655 103.802751 \nL 313.644504 218.825901 \nL 313.882065 204.320169 \nL 314.118353 160.460429 \nL 314.35338 151.089022 \nL 314.819707 221.122984 \nL 315.051034 32.201761 \nL 315.281152 189.021856 \nL 315.510074 165.572448 \nL 315.737814 178.842269 \nL 315.964383 173.165386 \nL 316.189793 197.900766 \nL 316.414056 181.260891 \nL 316.637183 180.642451 \nL 316.859186 186.598721 \nL 317.080076 181.462825 \nL 317.299865 169.254429 \nL 317.518563 174.700884 \nL 317.952729 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326.023178 210.134497 \nL 326.20268 149.603429 \nL 326.381453 198.182038 \nL 326.559504 128.535826 \nL 326.736838 220.276125 \nL 326.913462 195.661826 \nL 327.08938 225.632993 \nL 327.264599 224.490118 \nL 327.439124 208.922858 \nL 327.612961 220.686569 \nL 327.786115 182.490893 \nL 327.958591 218.219711 \nL 328.130394 124.957171 \nL 328.30153 224.829135 \nL 328.472005 151.156362 \nL 328.641822 218.194463 \nL 328.810987 215.581124 \nL 328.979506 156.849615 \nL 329.147382 191.214365 \nL 329.314622 189.529333 \nL 329.481229 215.93657 \nL 329.647208 212.434119 \nL 329.812565 216.715373 \nL 329.977304 84.316442 \nL 330.141429 217.897763 \nL 330.304945 212.978205 \nL 330.467857 106.161975 \nL 330.630168 208.015225 \nL 330.791884 114.237922 \nL 330.953009 223.479307 \nL 331.113546 195.088045 \nL 331.273501 197.982342 \nL 331.432878 179.655273 \nL 331.59168 220.682968 \nL 331.749912 205.193734 \nL 331.907577 206.53644 \nL 332.064681 223.273008 \nL 332.221227 218.141706 \nL 332.377218 118.880814 \nL 332.532659 207.132263 \nL 332.687554 198.726631 \nL 332.841906 111.055374 \nL 332.99572 218.808515 \nL 333.148998 224.912237 \nL 333.301746 189.469502 \nL 333.453965 225.787295 \nL 333.605661 222.49949 \nL 333.756836 117.503206 \nL 333.907494 208.592056 \nL 334.057639 154.918835 \nL 334.356403 208.30664 \nL 334.505029 159.079649 \nL 334.800786 194.167132 \nL 334.947923 201.396264 \nL 335.09457 226.036244 \nL 335.240731 214.143466 \nL 335.386409 146.111587 \nL 335.531607 222.294979 \nL 335.676328 165.403073 \nL 335.820576 202.657917 \nL 335.964352 71.483276 \nL 336.107662 211.978092 \nL 336.250506 134.593741 \nL 336.392889 219.073202 \nL 336.534814 125.56415 \nL 336.676283 223.607477 \nL 336.817299 218.863792 \nL 337.097985 169.100565 \nL 337.23766 173.803679 \nL 337.51569 219.74495 \nL 337.929472 150.275948 \nL 338.203185 209.903312 \nL 338.339406 198.61739 \nL 338.475207 156.602266 \nL 338.610592 215.735818 \nL 338.745561 159.783847 \nL 338.880119 153.06819 \nL 339.014267 219.616779 \nL 339.148007 47.856023 \nL 339.281343 207.221256 \nL 339.414277 162.323042 \nL 339.678948 218.442526 \nL 339.810689 214.274498 \nL 339.942038 188.861595 \nL 340.072997 199.351452 \nL 340.203567 183.975457 \nL 340.333752 183.850931 \nL 340.463554 191.256082 \nL 340.722015 220.903745 \nL 340.850679 223.679983 \nL 340.978969 57.304108 \nL 341.106887 218.21322 \nL 341.234434 222.568595 \nL 341.361613 125.222526 \nL 341.488426 221.01729 \nL 341.614875 175.218471 \nL 341.740963 218.352132 \nL 341.866691 144.630878 \nL 341.992061 210.345536 \nL 342.117075 123.150846 \nL 342.241736 221.253521 \nL 342.366045 185.437913 \nL 342.490004 225.891503 \nL 342.736882 206.116032 \nL 342.859804 203.463914 \nL 342.982384 130.185437 \nL 343.104624 217.219224 \nL 343.226526 217.286311 \nL 343.590222 134.126799 \nL 343.710789 220.969451 \nL 343.831028 170.504164 \nL 343.95094 209.081891 \nL 344.070526 164.200083 \nL 344.189789 221.922571 \nL 344.42735 217.855282 \nL 344.545653 223.898435 \nL 344.663638 113.671215 \nL 344.781308 220.073723 \nL 344.898665 207.683429 \nL 345.015711 177.464576 \nL 345.132446 223.104823 \nL 345.248873 79.639949 \nL 345.364993 217.070676 \nL 345.480808 220.882418 \nL 345.596319 162.226922 \nL 345.711528 169.249391 \nL 345.826437 212.49988 \nL 345.941047 151.846453 \nL 346.169377 219.463774 \nL 346.39653 152.282359 \nL 346.509668 216.972309 \nL 346.735078 187.801204 \nL 346.847352 176.252863 \nL 346.959341 219.312173 \nL 347.182468 165.140235 \nL 347.404471 215.897405 \nL 347.515055 209.409782 \nL 347.625362 213.676415 \nL 347.735393 207.612886 \nL 347.84515 215.699314 \nL 347.954635 148.61392 \nL 348.063848 194.821923 \nL 348.172792 174.733494 \nL 348.281466 218.031152 \nL 348.389873 61.438909 \nL 348.498015 214.124479 \nL 348.605891 176.579594 \nL 348.820855 199.322826 \nL 348.927945 145.750902 \nL 349.034776 206.948395 \nL 349.141348 111.069111 \nL 349.247663 222.67261 \nL 349.459526 165.208549 \nL 349.565077 217.113886 \nL 349.670376 155.579512 \nL 349.775424 199.496303 \nL 349.880222 189.621196 \nL 349.984771 218.905504 \nL 350.193129 158.576798 \nL 350.400506 195.930955 \nL 350.503829 157.02478 \nL 350.709753 224.033646 \nL 350.812355 161.793501 \nL 350.914718 204.588355 \nL 351.016845 93.848811 \nL 351.118735 227.86737 \nL 351.22039 222.279009 \nL 351.321812 124.768471 \nL 351.523957 226.216391 \nL 351.624683 228.246594 \nL 351.725179 179.060712 \nL 351.925486 218.251123 \nL 352.025299 223.27062 \nL 352.32339 179.594277 \nL 352.422307 220.220656 \nL 352.521002 219.624621 \nL 352.619477 177.448195 \nL 352.815769 219.462816 \nL 352.913589 188.754821 \nL 353.011191 209.908317 \nL 353.20575 154.328547 \nL 353.302708 166.177721 \nL 353.399454 211.589227 \nL 353.59231 144.311305 \nL 353.784326 220.753064 \nL 353.975508 176.622085 \nL 354.165865 223.530075 \nL 354.260736 143.065859 \nL 354.355403 219.370492 \nL 354.449867 185.54675 \nL 354.544129 203.475376 \nL 354.63819 190.318383 \nL 354.732051 154.605851 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220.524884 \nL 362.3741 161.683685 \nL 362.452863 206.639811 \nL 362.531485 159.065551 \nL 362.609966 212.892559 \nL 362.688309 126.061802 \nL 362.766512 222.04365 \nL 362.844577 151.792381 \nL 362.922503 226.657554 \nL 363.000293 181.887159 \nL 363.077945 216.806021 \nL 363.15546 124.390469 \nL 363.310083 229.874489 \nL 363.464166 176.393746 \nL 363.617711 217.610553 \nL 363.694284 215.139515 \nL 363.770724 214.540887 \nL 363.847031 222.26664 \nL 363.923207 179.657656 \nL 364.075164 222.94497 \nL 364.150946 119.017944 \nL 364.226599 219.021146 \nL 364.302121 155.900154 \nL 364.377515 201.828778 \nL 364.45278 123.22336 \nL 364.527916 224.797571 \nL 364.602925 218.707299 \nL 364.677806 226.928125 \nL 364.75256 225.272384 \nL 364.827188 228.121188 \nL 364.901689 215.259678 \nL 364.976065 158.408031 \nL 365.050315 201.161936 \nL 365.12444 181.939004 \nL 365.198441 174.027159 \nL 365.346071 204.839113 \nL 365.419701 154.569351 \nL 365.493208 214.661326 \nL 365.566593 163.747158 \nL 365.639856 206.964632 \nL 365.712997 152.427317 \nL 365.858916 223.870082 \nL 365.931695 220.577749 \nL 366.004354 229.016396 \nL 366.076893 212.696368 \nL 366.149313 228.842881 \nL 366.221614 225.681161 \nL 366.293797 227.693635 \nL 366.365861 223.206868 \nL 366.509638 155.200542 \nL 366.652947 222.478818 \nL 366.724427 227.09991 \nL 366.795792 218.856169 \nL 366.867041 227.498499 \nL 366.938175 223.317146 \nL 367.009194 223.730969 \nL 367.080099 168.011295 \nL 367.150891 208.701856 \nL 367.221568 149.002766 \nL 367.292133 213.712767 \nL 367.362585 210.190326 \nL 367.432924 214.337524 \nL 367.503151 211.34202 \nL 367.573266 143.999395 \nL 367.64327 209.63529 \nL 367.713163 187.830317 \nL 367.782946 180.783774 \nL 367.852618 153.994896 \nL 368.060975 198.565147 \nL 368.130209 147.835346 \nL 368.199335 212.628046 \nL 368.268352 163.923154 \nL 368.474758 222.295934 \nL 368.543346 177.639494 \nL 368.611827 203.365461 \nL 368.680201 225.093375 \nL 368.74847 182.925684 \nL 368.816633 206.510245 \nL 369.020493 140.257976 \nL 369.088237 221.164125 \nL 369.155877 181.640392 \nL 369.223414 172.501163 \nL 369.290847 220.096782 \nL 369.358177 176.171327 \nL 369.492529 222.11248 \nL 369.559552 118.128458 \nL 369.626473 221.173766 \nL 369.693293 208.78014 \nL 369.760011 193.158994 \nL 369.826629 212.696483 \nL 369.893146 167.767992 \nL 369.959563 217.415799 \nL 370.025879 135.00155 \nL 370.158214 219.390596 \nL 370.224233 220.58478 \nL 370.355975 153.588209 \nL 370.487324 219.643799 \nL 370.552852 140.679694 \nL 370.618282 225.107771 \nL 370.683616 204.298164 \nL 370.748853 173.697622 \nL 370.813993 193.167501 \nL 370.879038 205.81734 \nL 371.073597 166.373292 \nL 371.138259 197.455162 \nL 371.202827 170.694917 \nL 371.2673 221.32314 \nL 371.33168 184.964015 \nL 371.395965 210.522322 \nL 371.460156 144.18391 \nL 371.524255 183.88825 \nL 371.652172 198.965339 \nL 371.715992 143.863865 \nL 371.843355 224.307947 \nL 371.906898 113.417738 \nL 371.970351 218.750544 \nL 372.033712 214.874885 \nL 372.096982 177.462901 \nL 372.160161 224.9135 \nL 372.349157 152.681223 \nL 372.411976 218.979044 \nL 372.474706 139.485382 \nL 372.537346 220.215778 \nL 372.599898 169.605477 \nL 372.66236 194.504499 \nL 372.724735 184.469755 \nL 372.91133 226.968321 \nL 373.03529 135.045396 \nL 373.097139 220.083878 \nL 373.158901 152.084863 \nL 373.220577 175.506185 \nL 373.282167 224.212761 \nL 373.343671 161.976899 \nL 373.405089 210.683012 \nL 373.466422 217.757354 \nL 373.527669 98.126509 \nL 373.649909 223.925394 \nL 373.710903 126.06473 \nL 373.771811 201.948573 \nL 373.893377 170.308473 \nL 374.075099 214.027123 \nL 374.135507 225.822515 \nL 374.195832 217.593074 \nL 374.256075 221.786373 \nL 374.316235 162.202259 \nL 374.376314 227.803698 \nL 374.43631 220.881377 \nL 374.496225 220.644635 \nL 374.556059 81.634091 \nL 374.615812 223.147591 \nL 374.675483 195.17867 \nL 374.735074 165.585853 \nL 374.794585 202.737141 \nL 374.854015 149.811917 \nL 374.913365 220.320011 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SPS\n",
    "c=1\n",
    "gamma_max = 10\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "gamma = 1\n",
    "_,ff_star,_= SPS(cost, grad, hess, K, c, gamma_max, x0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SPS')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=1,label = 'Batch SPS', markevery=2000)\n",
    "plt.legend(fontsize=12)#字体大小\n",
    "plt.title(r\"Toy Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SPSlack\n",
    "gamma_max = 0.01\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "_,ff_star,_= SPSlack(cost, grad,hess, K, gamma_max , x0,s0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SPSlack')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=1,label = 'Batch SPSlack', markevery=2000)\n",
    "plt.legend(fontsize=12)#字体大小\n",
    "plt.title(r\"Optimization Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SPSALI\n",
    "gamma_max = 0.01\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "_,ff_star,_= SPSALI(cost, grad,hess, K, gamma_max , x0,s0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SPSALI')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=1,label = 'Batch SPSALI', markevery=2000)\n",
    "plt.legend(fontsize=12)#字体大小\n",
    "plt.title(r\"Optimization Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SPSL1\n",
    "gamma_max = 0.01\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "_,ff_star,_= SPSL1(cost, grad,hess, K, gamma_max , x0,s0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SPSL1')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=1,label = 'Batch SPSL1', markevery=2000)\n",
    "plt.legend(fontsize=12)#字体大小\n",
    "plt.title(r\"Optimization Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from method import SPSL2\n",
    "gamma_max = 0.01\n",
    "batch_size = 50\n",
    "K = 1000 #number of iterations\n",
    "_,ff_star,_= SPSL2(cost, grad,hess, K, gamma_max , x0,s0, batch_size, n)\n",
    "f_sol = ff_star[-1]\n",
    "\n",
    "#plotting angles\n",
    "fig, ax = plt.subplots()\n",
    "plt.xlabel('# iterations')\n",
    "plt.ylabel('cost SPSL2')\n",
    "plt.loglog(ff_star,'--',color = 'k',linewidth=1,label = 'Batch SPSL2', markevery=2000)\n",
    "plt.legend(fontsize=12)#字体大小\n",
    "plt.title(r\"Optimization Problem, d=\"+ str(d))\n",
    "ax.grid()"
   ]
  }
 ],
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