LinUCB.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from movielens import MovieLens\n",
    "from linUCB import LinUCB\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data\\movielens\\ml-100k.zip is already downloaded.\n",
      "Created a rating matrix of shape=(943, 1682) and dtype=float64 from u.data.\n",
      "Positive ratings (>=4) turned to 1, negative to -1, unknown to 0\n",
      "Created a genre matrix of shape=(1682, 19) and dtype=float64 from u.item.\n",
      "Created a titles matrix of shape=(1682,) and dtype=object from u.item.\n",
      "Statistics about self.R:\n",
      "Number of users:           943\n",
      "Number of items:           1682\n",
      "Total number of ratings:   1586126\n",
      "Known ratings:             100000\n",
      "Known positive ratings:    55375\n",
      "Known negative ratings:    44625\n",
      "Ratio of known ratings:    0.06304669364224531\n",
      "Ratio of positive ratings: 0.034912106604393346\n",
      "Ratio of negative ratings: 0.028134587037851974\n",
      "Avg number of positive ratings per user: 58.72216330858961 +- 54.67211827074995\n",
      "Avg number of negative ratings per user: 47.32237539766702 +- 58.41143787053165\n",
      "Shrinked rating matrix from (943, 1682) to (56, 100).\n",
      "\n",
      "After shrinking:\n",
      "Number of users:           56\n",
      "Number of items:           100\n",
      "Total number of ratings:   5600\n",
      "Known ratings:             903\n",
      "Known positive ratings:    606\n",
      "Known negative ratings:    297\n",
      "Ratio of known ratings:    0.16125\n",
      "Ratio of positive ratings: 0.10821428571428572\n",
      "Ratio of negative ratings: 0.05303571428571428\n",
      "Avg number of positive ratings per user: 10.821428571428571 +- 11.918034268130233\n",
      "Avg number of negative ratings per user: 5.303571428571429 +- 8.209140469312118\n",
      "\n",
      "Initializing matrix A of shape (100, 119, 119) which will require 11.3288MB of memory.\n",
      "\n",
      "LinUCB successfully initialized.\n"
     ]
    }
   ],
   "source": [
    "ucb = LinUCB(alpha=0.1, dataset=None, max_items=100, allow_selecting_known_arms=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R:\n",
      " [[ 1. -1.  1. ...,  1. -1.  1.]\n",
      " [ 1.  0.  0. ...,  0.  0.  1.]\n",
      " [ 0.  0.  0. ...,  0.  0.  0.]\n",
      " ..., \n",
      " [ 1.  0.  0. ...,  0.  0.  1.]\n",
      " [ 0.  0.  0. ...,  0.  0.  0.]\n",
      " [ 1.  0.  0. ...,  1.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "print('R:\\n', ucb.dataset.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished epoch 0/50 with avg reward 0.6071428571428571 in 1.552785873413086s\n",
      "Finished epoch 1/50 with avg reward 0.6607142857142857 in 1.503936767578125s\n",
      "Finished epoch 2/50 with avg reward 0.6607142857142857 in 1.4646108150482178s\n",
      "Finished epoch 3/50 with avg reward 0.75 in 1.5237205028533936s\n",
      "Finished epoch 4/50 with avg reward 0.7857142857142857 in 1.512455940246582s\n",
      "Finished epoch 5/50 with avg reward 0.7678571428571429 in 1.4529874324798584s\n",
      "Finished epoch 6/50 with avg reward 0.75 in 1.4491147994995117s\n",
      "Finished epoch 7/50 with avg reward 0.7857142857142857 in 1.452491283416748s\n",
      "Finished epoch 8/50 with avg reward 0.7857142857142857 in 1.4747285842895508s\n",
      "Finished epoch 9/50 with avg reward 0.8035714285714286 in 1.5306973457336426s\n",
      "Finished epoch 10/50 with avg reward 0.8392857142857143 in 1.6003155708312988s\n",
      "Finished epoch 11/50 with avg reward 0.8571428571428571 in 1.5510241985321045s\n",
      "Finished epoch 12/50 with avg reward 0.8392857142857143 in 1.5619399547576904s\n",
      "Finished epoch 13/50 with avg reward 0.8571428571428571 in 1.480229139328003s\n",
      "Finished epoch 14/50 with avg reward 0.8571428571428571 in 1.5599474906921387s\n",
      "Finished epoch 15/50 with avg reward 0.8571428571428571 in 1.5314569473266602s\n",
      "Finished epoch 16/50 with avg reward 0.8571428571428571 in 1.5440802574157715s\n",
      "Finished epoch 17/50 with avg reward 0.8571428571428571 in 1.518200159072876s\n",
      "Finished epoch 18/50 with avg reward 0.8928571428571429 in 1.4871973991394043s\n",
      "Finished epoch 19/50 with avg reward 0.8928571428571429 in 1.4307353496551514s\n",
      "Finished epoch 20/50 with avg reward 0.8928571428571429 in 1.4712302684783936s\n",
      "Finished epoch 21/50 with avg reward 0.8928571428571429 in 1.561948537826538s\n",
      "Finished epoch 22/50 with avg reward 0.875 in 1.5917258262634277s\n",
      "Finished epoch 23/50 with avg reward 0.8928571428571429 in 1.5000195503234863s\n",
      "Finished epoch 24/50 with avg reward 0.8928571428571429 in 1.4894251823425293s\n",
      "Finished epoch 25/50 with avg reward 0.8928571428571429 in 1.4842913150787354s\n",
      "Finished epoch 26/50 with avg reward 0.8928571428571429 in 1.5156621932983398s\n",
      "Finished epoch 27/50 with avg reward 0.8928571428571429 in 1.4598205089569092s\n",
      "Finished epoch 28/50 with avg reward 0.9107142857142857 in 1.5435237884521484s\n",
      "Finished epoch 29/50 with avg reward 0.9107142857142857 in 1.5571162700653076s\n",
      "Finished epoch 30/50 with avg reward 0.9107142857142857 in 1.4766385555267334s\n",
      "Finished epoch 31/50 with avg reward 0.9107142857142857 in 1.479438066482544s\n",
      "Finished epoch 32/50 with avg reward 0.9107142857142857 in 1.5288116931915283s\n",
      "Finished epoch 33/50 with avg reward 0.9107142857142857 in 1.4459714889526367s\n",
      "Finished epoch 34/50 with avg reward 0.9107142857142857 in 1.4856929779052734s\n",
      "Finished epoch 35/50 with avg reward 0.9107142857142857 in 1.5330607891082764s\n",
      "Finished epoch 36/50 with avg reward 0.9107142857142857 in 1.483243465423584s\n",
      "Finished epoch 37/50 with avg reward 0.9107142857142857 in 1.440375804901123s\n",
      "Finished epoch 38/50 with avg reward 0.9107142857142857 in 1.4579293727874756s\n",
      "Finished epoch 39/50 with avg reward 0.9107142857142857 in 1.446725606918335s\n",
      "Finished epoch 40/50 with avg reward 0.9107142857142857 in 1.5060577392578125s\n",
      "Finished epoch 41/50 with avg reward 0.9107142857142857 in 1.5212090015411377s\n",
      "Finished epoch 42/50 with avg reward 0.9107142857142857 in 1.4816653728485107s\n",
      "Finished epoch 43/50 with avg reward 0.9107142857142857 in 1.459599256515503s\n",
      "Finished epoch 44/50 with avg reward 0.9107142857142857 in 1.4446063041687012s\n",
      "Finished epoch 45/50 with avg reward 0.9107142857142857 in 1.5518925189971924s\n",
      "Finished epoch 46/50 with avg reward 0.9285714285714286 in 1.4647176265716553s\n",
      "Finished epoch 47/50 with avg reward 0.9285714285714286 in 1.55332612991333s\n",
      "Finished epoch 48/50 with avg reward 0.9285714285714286 in 1.4004156589508057s\n",
      "Finished epoch 49/50 with avg reward 0.9285714285714286 in 1.4852497577667236s\n"
     ]
    }
   ],
   "source": [
    "avg_reward = ucb.run(num_epochs=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x13bdfee8828>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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l6SJJuzdg37OBwqFOeqbLCs0CRkfEioiYDzwL7FV9RxExIiLKI6K8e/fuDQjB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\nZrnhpGdmZrnhpGdmZrnhpGdmZrnx/wGnOxF5sjDALAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13bdfe90668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pylab import rcParams\n",
    "rcParams['figure.figsize'] = 7, 5\n",
    "plt.plot(range(len(avg_reward)), avg_reward)\n",
    "plt.ylabel('average reward in epoch')\n",
    "plt.ylim(0.2, 1)\n",
    "plt.xlabel('epoch (1 epoch = recommended to all users)')\n",
    "plt.title('LinUCB: Fixed rewards')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data\\movielens\\ml-100k.zip is already downloaded.\n",
      "Created a rating matrix of shape=(943, 1682) and dtype=float64 from u.data.\n",
      "Positive ratings (>=4) turned to 1, negative to -1, unknown to 0\n",
      "Created a genre matrix of shape=(1682, 19) and dtype=float64 from u.item.\n",
      "Created a titles matrix of shape=(1682,) and dtype=object from u.item.\n",
      "Statistics about self.R:\n",
      "Number of users:           943\n",
      "Number of items:           1682\n",
      "Total number of ratings:   1586126\n",
      "Known ratings:             100000\n",
      "Known positive ratings:    55375\n",
      "Known negative ratings:    44625\n",
      "Ratio of known ratings:    0.06304669364224531\n",
      "Ratio of positive ratings: 0.034912106604393346\n",
      "Ratio of negative ratings: 0.028134587037851974\n",
      "Avg number of positive ratings per user: 58.72216330858961 +- 54.67211827074995\n",
      "Avg number of negative ratings per user: 47.32237539766702 +- 58.41143787053165\n",
      "Shrinked rating matrix from (943, 1682) to (56, 100).\n",
      "\n",
      "After shrinking:\n",
      "Number of users:           56\n",
      "Number of items:           100\n",
      "Total number of ratings:   5600\n",
      "Known ratings:             903\n",
      "Known positive ratings:    606\n",
      "Known negative ratings:    297\n",
      "Ratio of known ratings:    0.16125\n",
      "Ratio of positive ratings: 0.10821428571428572\n",
      "Ratio of negative ratings: 0.05303571428571428\n",
      "Avg number of positive ratings per user: 10.821428571428571 +- 11.918034268130233\n",
      "Avg number of negative ratings per user: 5.303571428571429 +- 8.209140469312118\n",
      "\n",
      "Initializing matrix A of shape (100, 119, 119) which will require 11.3288MB of memory.\n",
      "\n",
      "LinUCB successfully initialized.\n"
     ]
    }
   ],
   "source": [
    "ucb_stochastic = LinUCB(alpha=0.1, dataset=None, max_items=100, \n",
    "                        allow_selecting_known_arms=True, fixed_rewards=False, prob_reward_p=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R:\n",
      " [[ 1. -1.  1. ...,  1. -1.  1.]\n",
      " [ 1.  0.  0. ...,  0.  0.  1.]\n",
      " [ 0.  0.  0. ...,  0.  0.  0.]\n",
      " ..., \n",
      " [ 1.  0.  0. ...,  0.  0.  1.]\n",
      " [ 0.  0.  0. ...,  0.  0.  0.]\n",
      " [ 1.  0.  0. ...,  1.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "print('R:\\n', ucb_stochastic.dataset.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished epoch 0/50 with avg reward 0.42857142857142855 in 1.423952579498291s\n",
      "Finished epoch 1/50 with avg reward 0.5535714285714286 in 1.4462800025939941s\n",
      "Finished epoch 2/50 with avg reward 0.5178571428571429 in 1.4531726837158203s\n",
      "Finished epoch 3/50 with avg reward 0.6428571428571429 in 1.4564926624298096s\n",
      "Finished epoch 4/50 with avg reward 0.6785714285714286 in 1.4292511940002441s\n",
      "Finished epoch 5/50 with avg reward 0.6785714285714286 in 1.4329595565795898s\n",
      "Finished epoch 6/50 with avg reward 0.6071428571428571 in 1.5166280269622803s\n",
      "Finished epoch 7/50 with avg reward 0.7142857142857143 in 1.5158579349517822s\n",
      "Finished epoch 8/50 with avg reward 0.7321428571428571 in 1.5242359638214111s\n",
      "Finished epoch 9/50 with avg reward 0.6785714285714286 in 1.4195635318756104s\n",
      "Finished epoch 10/50 with avg reward 0.75 in 1.423771858215332s\n",
      "Finished epoch 11/50 with avg reward 0.8035714285714286 in 1.5463316440582275s\n",
      "Finished epoch 12/50 with avg reward 0.8035714285714286 in 1.5004987716674805s\n",
      "Finished epoch 13/50 with avg reward 0.75 in 1.4027862548828125s\n",
      "Finished epoch 14/50 with avg reward 0.7321428571428571 in 1.5803709030151367s\n",
      "Finished epoch 15/50 with avg reward 0.7678571428571429 in 1.541501760482788s\n",
      "Finished epoch 16/50 with avg reward 0.8392857142857143 in 1.5591683387756348s\n",
      "Finished epoch 17/50 with avg reward 0.8214285714285714 in 1.4493193626403809s\n",
      "Finished epoch 18/50 with avg reward 0.75 in 1.446549654006958s\n",
      "Finished epoch 19/50 with avg reward 0.8392857142857143 in 1.465177059173584s\n",
      "Finished epoch 20/50 with avg reward 0.7857142857142857 in 1.466484785079956s\n",
      "Finished epoch 21/50 with avg reward 0.8392857142857143 in 1.4695732593536377s\n",
      "Finished epoch 22/50 with avg reward 0.875 in 1.4436159133911133s\n",
      "Finished epoch 23/50 with avg reward 0.8392857142857143 in 1.502685546875s\n",
      "Finished epoch 24/50 with avg reward 0.8392857142857143 in 1.5135478973388672s\n",
      "Finished epoch 25/50 with avg reward 0.7678571428571429 in 1.4488627910614014s\n",
      "Finished epoch 26/50 with avg reward 0.8392857142857143 in 1.4726719856262207s\n",
      "Finished epoch 27/50 with avg reward 0.8571428571428571 in 1.4377691745758057s\n",
      "Finished epoch 28/50 with avg reward 0.8392857142857143 in 1.4314370155334473s\n",
      "Finished epoch 29/50 with avg reward 0.875 in 1.4730243682861328s\n",
      "Finished epoch 30/50 with avg reward 0.875 in 1.5121488571166992s\n",
      "Finished epoch 31/50 with avg reward 0.9107142857142857 in 1.4472377300262451s\n",
      "Finished epoch 32/50 with avg reward 0.9107142857142857 in 1.521090030670166s\n",
      "Finished epoch 33/50 with avg reward 0.875 in 1.419341802597046s\n",
      "Finished epoch 34/50 with avg reward 0.8571428571428571 in 1.5445048809051514s\n",
      "Finished epoch 35/50 with avg reward 0.875 in 1.5442349910736084s\n",
      "Finished epoch 36/50 with avg reward 0.8928571428571429 in 1.5073223114013672s\n",
      "Finished epoch 37/50 with avg reward 0.8928571428571429 in 1.4788422584533691s\n",
      "Finished epoch 38/50 with avg reward 0.9107142857142857 in 1.510094404220581s\n",
      "Finished epoch 39/50 with avg reward 0.8571428571428571 in 1.639073133468628s\n",
      "Finished epoch 40/50 with avg reward 0.875 in 1.602083683013916s\n",
      "Finished epoch 41/50 with avg reward 0.8392857142857143 in 1.536860704421997s\n",
      "Finished epoch 42/50 with avg reward 0.8392857142857143 in 1.6031217575073242s\n",
      "Finished epoch 43/50 with avg reward 0.8035714285714286 in 1.495967149734497s\n",
      "Finished epoch 44/50 with avg reward 0.875 in 1.4956600666046143s\n",
      "Finished epoch 45/50 with avg reward 0.8214285714285714 in 1.5254406929016113s\n",
      "Finished epoch 46/50 with avg reward 0.8214285714285714 in 1.5300877094268799s\n",
      "Finished epoch 47/50 with avg reward 0.8928571428571429 in 1.4529578685760498s\n",
      "Finished epoch 48/50 with avg reward 0.875 in 1.4527220726013184s\n",
      "Finished epoch 49/50 with avg reward 0.8392857142857143 in 1.4494407176971436s\n"
     ]
    }
   ],
   "source": [
    "avg_reward_stochastic = ucb_stochastic.run(num_epochs=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x13bdff79cc0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hORFZ0jOdVnF5FWt2HTgyXqhHtzBeuj6VealJPPnBNm7+x9rjWjCzqLySzPwS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\nekEQBEFuCKcXBEEQ5Ib/AaW1E2Zaca+wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13bdfe99198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(avg_reward_stochastic)), avg_reward_stochastic)\n",
    "plt.ylabel('average reward in epoch')\n",
    "plt.ylim(0.2, 1)\n",
    "plt.xlabel('epoch (1 epoch = recommended to all users)')\n",
    "plt.title('LinUCB: Stochastic rewards with p=0.9')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}