{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using different learning schedules\n",
    "`lightfm` implements two learning schedules: adagrad and adadelta. Neither is clearly superior, and, like other hyperparameter choices, the best learning schedule will differ based on the problem at hand.\n",
    "\n",
    "This example tries both at the Movielens 100k dataset.\n",
    "\n",
    "## Preliminaries\n",
    "Let's first get the data and define the evaluations functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import data\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from lightfm import LightFM\n",
    "from lightfm.datasets import fetch_movielens\n",
    "from lightfm.evaluation import auc_score\n",
    "\n",
    "movielens = fetch_movielens()\n",
    "\n",
    "train, test = movielens['train'], movielens['test']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment\n",
    "To evaluate the performance of both learning schedules, let's create two models and run each for a number of epochs, measuring the ROC AUC on the test set at the end of each epoch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alpha = 1e-3\n",
    "epochs = 70\n",
    "\n",
    "adagrad_model = LightFM(no_components=30,\n",
    "                        loss='warp',\n",
    "                        learning_schedule='adagrad',\n",
    "                        user_alpha=alpha,\n",
    "                        item_alpha=alpha)\n",
    "adadelta_model = LightFM(no_components=30,\n",
    "                        loss='warp',\n",
    "                        learning_schedule='adadelta',\n",
    "                        user_alpha=alpha,\n",
    "                        item_alpha=alpha)\n",
    "\n",
    "adagrad_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    adagrad_model.fit_partial(train, epochs=1)\n",
    "    adagrad_auc.append(auc_score(adagrad_model, test).mean())\n",
    "    \n",
    "    \n",
    "adadelta_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    adadelta_model.fit_partial(train, epochs=1)\n",
    "    adadelta_auc.append(auc_score(adadelta_model, test).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the adadelta gets to a better result at the beginning of training. However, as we keep running more epochs adagrad wins out, converging to a better final solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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MpX1+k8YYM9iICKra48v3nbJl7z7QejfwLhAMvKCq20XkTvf254AfA4tFZCNO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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79d824ed10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(len(adagrad_auc))\n",
    "plt.plot(x, np.array(adagrad_auc))\n",
    "plt.plot(x, np.array(adadelta_auc))\n",
    "plt.legend(['adagrad', 'adadelta'], loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can try the same for the k-OS loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alpha = 1e-3\n",
    "epochs = 70\n",
    "\n",
    "adagrad_model = LightFM(no_components=30,\n",
    "                        loss='warp-kos',\n",
    "                        learning_schedule='adagrad',\n",
    "                        user_alpha=alpha, item_alpha=alpha)\n",
    "adadelta_model = LightFM(no_components=30,\n",
    "                        loss='warp-kos',\n",
    "                        learning_schedule='adadelta',\n",
    "                        user_alpha=alpha, item_alpha=alpha)\n",
    "\n",
    "adagrad_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    adagrad_model.fit_partial(train, epochs=1)\n",
    "    adagrad_auc.append(auc_score(adagrad_model, test).mean())\n",
    "    \n",
    "    \n",
    "adadelta_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    adadelta_model.fit_partial(train, epochs=1)\n",
    "    adadelta_auc.append(auc_score(adadelta_model, test).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0hIV1d0TGGBNYAiLZZ7gyGB1v/fXGGNNRAZHsM12ZjIwfaf31xhjTQQGR7PPL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79d824e950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(len(adagrad_auc))\n",
    "plt.plot(x, np.array(adagrad_auc))\n",
    "plt.plot(x, np.array(adadelta_auc))\n",
    "plt.legend(['adagrad', 'adadelta'], loc='lower right')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}