Step3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Step 3: Optimization with uncertain conversion rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# fixed graph weights (same click influence probabilities between the products for each user)\n",
    "# homogeneous users (one class with small variability)\n",
    "# fixed alphas (same number of users each day distributed equally between the initial webpages)\n",
    "# uncertain conversion rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from Environment.E_commerce import *\n",
    "from Algorithms.Conv_rates_Learner import *\n",
    "from Algorithms.Greedy_Learner import *\n",
    "from Algorithms.TS_Learner import *\n",
    "from Algorithms.UCB_Learner import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Margin matrix: \n",
      "[[ 3.998  5.998  7.998 10.998]\n",
      " [ 5.998  8.598 11.998 15.998]\n",
      " [ 7.797 10.797 13.797 16.797]\n",
      " [15.596 20.596 23.596 26.596]\n",
      " [39.995 49.995 59.995 69.995]]\n"
     ]
    }
   ],
   "source": [
    "P1 = Product(0,[19.99, 21.99, 23.99, 26.99],np.multiply([0.2, 0.2, 0.2, 0.2],[19.99, 19.99, 19.99, 19.99])+[0, 21.99-19.99, 23.99-19.99, 26.99-19.99])\n",
    "# t-shirt\n",
    "P2 = Product(1,[29.99, 32.59, 35.99, 39.99],np.multiply([0.2, 0.2, 0.2, 0.2],[29.99, 29.99, 29.99, 29.99])+[29.99, 32.59, 35.99, 39.99]-29.99)\n",
    "# shirt\n",
    "P3 = Product(2,[25.99,28.99, 31.99, 34.99],np.multiply([0.3, 0.3, 0.3, 0.3],[25.99,25.99, 25.99, 25.99])+[25.99,28.99, 31.99, 34.99]-25.99)\n",
    "# shorts\n",
    "P4 = Product(3,[38.99,43.99,46.99, 49.99],np.multiply([0.4, 0.4, 0.4, 0.4],[38.99,38.99,38.99, 38.99])+[38.99,43.99,46.99, 49.99]-38.99)\n",
    "# pants\n",
    "P5 = Product(4,[79.99,89.99, 99.99, 109.99],np.multiply([0.5, 0.5, 0.5, 0.5],[79.99,79.99, 79.99, 79.99])+[79.99,89.99, 99.99, 109.99]-79.99)\n",
    "# shoes\n",
    "\n",
    "products = [P1,P2,P3,P4,P5]\n",
    "margins_matrix = np.zeros((5,4))\n",
    "for i in range(5):\n",
    "    for j in range(4):\n",
    "        margins_matrix[i,j] = products[i].margins_list[j]\n",
    "print(\"Margin matrix: \")\n",
    "print(margins_matrix)\n",
    "\n",
    "E = E_commerce()\n",
    "E.graph = np.array([[0. , 0., 1. , 0.5 , 0. ],[0. , 0. , 0.5 , 1., 0. ],[0.5 , 1. , 0. , 0. , 0. ],[1. , 0.5 , 0. , 0. , 0. ],[0. , 0.5 , 0. , 1. , 0. ]])\n",
    "E.set_products(products)\n",
    "E.set_lambda(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Using a simple algorithm trained for a long time (1000 days, repeated 10 times), we obtain an estimation of conversion rates and expected rewards of the arms for each product. This will be considered our clairvoyant solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Conversion rates\n",
      "[[0.8230333  0.41427134 0.09976588 0.00162077]\n",
      " [0.84880662 0.45943562 0.06230299 0.0006476 ]\n",
      " [0.94621639 0.55360727 0.10389332 0.00343537]\n",
      " [0.95903458 0.52388244 0.17042796 0.02210472]\n",
      " [0.99663556 0.70677187 0.29361887 0.02023444]]\n",
      "_______________________________________________\n",
      "Rewards per arm of this simple algorithm\n",
      "[[ 6.58222894  4.96491952  1.59202229  0.03146815]\n",
      " [ 5.09097232  3.94685151  0.74559022  0.00792949]\n",
      " [22.13955129 17.93907529  4.29496675  0.16152497]\n",
      " [44.87795481 32.29535342 12.0259853   1.73422302]\n",
      " [39.86755508 35.32447457 17.61887666  1.40124957]]\n",
      "Expected rewards per arm = margin * conversion rate\n",
      "[[ 3.29048714  2.48479948  0.7979275   0.01782527]\n",
      " [ 5.0911421   3.95022746  0.74751122  0.01036033]\n",
      " [ 7.37764923  5.97729771  1.4334161   0.05770385]\n",
      " [14.95710333 10.78988281  4.02141819  0.58789717]\n",
      " [39.86043927 35.33505952 17.61566424  1.41630947]]\n",
      "_______________________________________________\n",
      "Expected units sold per arm\n",
      "[[2.  2.  2.  2. ]\n",
      " [1.  1.  1.  0.9]\n",
      " [3.  3.  3.  3. ]\n",
      " [3.  3.  3.  3. ]\n",
      " [1.  1.  1.  1. ]]\n",
      "_______________________________________________\n",
      "Best configuration [0. 0. 0. 0. 0.]\n",
      "Optimal cumulative expected reward per round\n",
      "118.53681335150561\n"
     ]
    }
   ],
   "source": [
    "# Random algorithm which for each round pulls a random choice\n",
    "# to estimate asymptotically the conv_rates and the mean of the number of units sold per product,\n",
    "# useful for computing clairvoyant solution and regrets of the bandit algorithms\n",
    "\n",
    "\n",
    "n_arms = 4\n",
    "num_users = 100 #mean number of users for each day\n",
    "n_days = 1000\n",
    "fixed_alpha = 1\n",
    "fixed_weights = 1\n",
    "fixed_units = 1\n",
    "num_experiments = 10\n",
    "opt_vector = np.zeros(num_experiments)\n",
    "conv_rates_per_experiment = []\n",
    "mean_units_sold_per_product_per_experiment = []\n",
    "cr_learner_expected_rewards_per_experiment = []\n",
    "\n",
    "for e in range(num_experiments):\n",
    "    env = Environment(n_arms, E, margins_matrix, num_users, fixed_alpha, fixed_weights,fixed_units)\n",
    "    cr_learner = Conv_rates(n_arms=n_arms)\n",
    "\n",
    "    for d in range(n_days):\n",
    "\n",
    "        pulled_arm = cr_learner.pull_arm()\n",
    "        reward = env.round(pulled_arm)\n",
    "        cr_learner.update(pulled_arm, reward, env.clicks_current_day, env.purchases_current_day,env.daily_units)\n",
    "\n",
    "\n",
    "    conversion_rates = np.zeros((5,4))\n",
    "    np.set_printoptions(suppress=True)\n",
    "    for i in range(5):\n",
    "        conversion_rates[i] = cr_learner.beta_parameters[i][:,0]/(cr_learner.beta_parameters[i][:,0]+cr_learner.beta_parameters[i][:,1])\n",
    "        opt_vector[e] += np.max(np.array(E.products[i].margins_list) * conversion_rates[i] * cr_learner.lambda_poisson[i])\n",
    "\n",
    "    conv_rates_per_experiment.append(conversion_rates)\n",
    "    mean_units_sold_per_product_per_experiment.append(cr_learner.lambda_poisson)\n",
    "    cr_learner_expected_rewards_per_experiment.append(cr_learner.expected_rewards)\n",
    "\n",
    "#optimal expected clarvoyant solution is given choosing each round the best combination\n",
    "opt = np.mean(opt_vector) #+ np.std(opt_vector)\n",
    "best_arm_per_product = np.zeros(5)\n",
    "for i in range(5):   \n",
    "    best_arm_per_product[i] = np.argmax(np.array(E.products[i].margins_list) * np.mean(conv_rates_per_experiment,axis=0)[i]\n",
    "                                        * np.mean(mean_units_sold_per_product_per_experiment, axis = 0)[i])#expected_units_sold_per_product[i])#\n",
    "    \n",
    "print(\"_______________________________________________\")\n",
    "print(\"Conversion rates\")\n",
    "print(np.mean(conv_rates_per_experiment,axis=0))\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Rewards per arm of this simple algorithm\")\n",
    "print(np.mean(cr_learner_expected_rewards_per_experiment,axis=0))\n",
    "print(\"Expected rewards per arm = margin * conversion rate\")\n",
    "print(margins_matrix*np.mean(conv_rates_per_experiment,axis=0))\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Expected units sold per arm\")\n",
    "print(np.mean(mean_units_sold_per_product_per_experiment, axis = 0))\n",
    "\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Best configuration\", best_arm_per_product)\n",
    "print(\"Optimal cumulative expected reward per round\")\n",
    "print(opt) # optimal configuration: the best combination of arms\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "118.53681335150561"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Thompson Sampling: optimization of the cumulative expected margin over all the products"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Margin matrix: \n",
      "[[ 3.998  5.998  7.998 10.998]\n",
      " [ 5.998  8.598 11.998 15.998]\n",
      " [ 7.797 10.797 13.797 16.797]\n",
      " [15.596 20.596 23.596 26.596]\n",
      " [39.995 49.995 59.995 69.995]]\n",
      "Estimated conversion rates: \n",
      "[[0.8230333  0.41427134 0.09976588 0.00162077]\n",
      " [0.84880662 0.45943562 0.06230299 0.0006476 ]\n",
      " [0.94621639 0.55360727 0.10389332 0.00343537]\n",
      " [0.95903458 0.52388244 0.17042796 0.02210472]\n",
      " [0.99663556 0.70677187 0.29361887 0.02023444]]\n",
      "Expected rewards per arm = margin * conversion rate \n",
      "[[ 3.29048714  2.48479948  0.7979275   0.01782527]\n",
      " [ 5.0911421   3.95022746  0.74751122  0.01036033]\n",
      " [ 7.37764923  5.97729771  1.4334161   0.05770385]\n",
      " [14.95710333 10.78988281  4.02141819  0.58789717]\n",
      " [39.86043927 35.33505952 17.61566424  1.41630947]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Margin matrix: \")\n",
    "print(margins_matrix)\n",
    "print(\"Estimated conversion rates: \")\n",
    "print(np.mean(conv_rates_per_experiment,axis=0))\n",
    "print(\"Expected rewards per arm = margin * conversion rate \")\n",
    "print(np.mean(conv_rates_per_experiment,axis=0)*margins_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Thompson Sampling\n",
    "# Comparison between TS and UCB\n",
    "\n",
    "n_arms = 4\n",
    "num_users = 100\n",
    "n_days = 365\n",
    "fixed_alpha = 1\n",
    "fixed_weights = 1\n",
    "fixed_units = 1\n",
    "n_experiments = 20\n",
    "\n",
    "ts_rewards_per_experiment = []\n",
    "ts_rewards_per_day = np.zeros(n_days)\n",
    "\n",
    "for e in range(n_experiments):\n",
    "\n",
    "    env = Environment(n_arms, E, margins_matrix, num_users, fixed_alpha,fixed_weights,fixed_units)\n",
    "    ts_learner = TS(n_arms=n_arms)\n",
    "\n",
    "    for d in range(n_days):\n",
    "\n",
    "        pulled_arm = ts_learner.pull_arm(env.margins_matrix)\n",
    "        reward = env.round(pulled_arm)\n",
    "        ts_learner.update(pulled_arm, reward, env.clicks_current_day, env.purchases_current_day, env.daily_units)\n",
    "        ts_rewards_per_day[d] += np.sum(reward)\n",
    "    \n",
    "\n",
    "    ts_rewards_per_experiment.append(ts_learner.collected_rewards)\n",
    "\n",
    "\n",
    "ts_rewards_per_day = ts_rewards_per_day/n_experiments\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"Regret\")\n",
    "plt.plot(np.cumsum(np.mean(opt - ts_rewards_per_experiment, axis=0)), 'r')\n",
    "plt.legend([\"TS\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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T7rGU4F13xYpSEybAt76VdVUiIntELf72WrYMPvEJmDo1Zrb8/vfht7/VOHsRKTlq8bfHgw/GFbQA3/xmhH+FvjNFpDQp+NviHhOhnX8+vO99MQa/6YVWIiIlSM3W1mzeDCedFLd+/WJOHYW+iJQBBf/ONm6Ea6+FD30oFhT/xjfgkUfgwAOzrkxEpFOkuQJXL+BxoGeyn1+7+7VmNgC4BxhBLMQysaXF1rucO9x3H0yZAi+/HK373/0Ozjwz68pERDpVmi3+d4FT3P1YYDQwwczGApOBh919JPBw8jx7V14ZffnuMWna8uUKfREpS6kFv4ctydPuyc2Bc4CZyfaZwLlp1dAu7vCLX8APfgCXXRYza55ySqYliYikKdU+fjOrNLMFwFpgjrs/DQxuXGw9uW9hJjMws0lmNs/M5tXU1KRX5I9/DJ/8JBx3HNx0U8yiKSJSxlINfnevd/fRwFBgjJm1e/kod5/u7tXuXl2V1vqxS5bANdfA6afD00/HVMoiImWuS0b1uPtG4FFgArDGzIYAJPdru6KGnQqCP/4RTj45VsS69VZdgSsiuZFa8JtZlZntnzzuDYwH/gHMBi5O3nYxcH9aNbRo0yY499w4cduvXwzV1IpXIpIjaXZoDwFmmlkl8QUzy91/b2ZzgVlmdimwHPh4ijXsasoU+MMf4LvfhS99CXr16tLdi4hkLbXgd/eFwHEtbF8PnJrWfttUXw+//nXMu/O1r2VSgohI1vJ15e7cubBmzY4J10REcihfwX/77bDvvnDWWVlXIiKSmfwE/+rVcPfd8JnPxEldEZGcyk/wP/gg1NbCZz+bdSUiIpnKT/A/9hgMGgSj2n0NmYhIWcpX8J98slbOEpHcy0cKbtgAr78OY8dmXYmISObyEfzbt8f9vvtmW4eISBHIR/DX18d9ZWW2dYiIFAEFv4hIzij4RURyRsEvIpIz+Qj+urq4V/CLiOQk+NXiFxEpUPCLiORMmitwDTOzR8xssZm9aGZfTrZPNbM3zWxBckt/qkwFv4hIQZorcNUBX3H358ysLzDfzOYkr93i7jemuO/mFPwiIgVprsC1CliVPN5sZouBg9LaX5sag79bmt9zIiKloUv6+M1sBLEM49PJpsvNbKGZ3WFm/VMvQC1+EZGC1IPfzPoAvwGudPdNwK3AocBo4i+Cm1r53CQzm2dm82pqavauCAW/iEhBqsFvZt2J0P+5u98L4O5r3L3e3RuA24ExLX3W3ae7e7W7V1dVVe1dIQp+EZGCNEf1GDADWOzuNzfZPqTJ284DFqVVQ4GCX0SkIM2znScBnwJeMLMFybYpwEVmNhpw4HXg8ynWEBT8IiIFaY7qeRKwFl56IK19tkrBLyJSoCt3RURyRsEvIpIzCn4RkZxpV/A3zrOzu21FS8EvIlLQ3hb/xS1su6QT60iXgl9EpKDNUT1mdhHwCeBgM5vd5KW+wPo0C+tUCn4RkYLdDed8iphWYRDNp1bYDCxMq6hOp+AXESloM/jdfRmwDPgXM3svMNLd/2xmvYHexBdA8VPwi4gUtPfk7ueAXwO3JZuGAr9NqabOp+AXESlo78ndLxJTMGwCcPdXgAPSKqrTKfhFRAraG/zvuvv2xidm1o2Ya6c01NXFvYJfRKTdwf+YmU0BepvZacCvgN+lV1YnU4tfRKSgvcF/NVADvEDMpvkA8I20iup0Cn4RkYLdzs5pZhXAQncfRSycUnoU/CIiBbtt8ScrZT1vZsO7oJ50aLF1EZGC9ibhEOBFM3sGeLtxo7ufnUpVnU0tfhGRgvYG/7f29Aeb2TDgTuBAoAGY7u7fN7MBwD3ACGIFronuvmFPf/4eUfCLiBS0K/jd/bEO/Ow64Cvu/pyZ9QXmm9kcYnK3h919mplNBiYTJ4/To+AXESlo75W7m81s0063N8zsPjM7pKXPuPsqd38uebwZWAwcBJwDzEzeNhM4d69/i91pDP6KfCw/ICLSlvZ29dwMrAR+QayjeyHRhfMScAcwrq0Pm9kI4DjgaWCwu6+C+HIwsxavADazScAkgOHD9/K8cn29WvsiIon2NoEnuPtt7r7Z3Te5+3TgLHe/B+jf1gfNrA/wG+BKd9/U3sLcfbq7V7t7dVVVVXs/1jIFv4hIQXuDv8HMJppZRXKb2OS1VqduMLPuROj/3N3vTTavMbMhyetDgLUdKXyPKPhFRAraG/yfBD5FhPSa5PG/JdMzX97SB8zMgBnAYne/uclLs9mxotfFwP0dqHvPKPhFRAraO6rnNeB/t/Lyk61sP4n4gnjBzBYk26YA04BZZnYpsBz4eLur7SgFv4hIQbuC38wOB24lTsyOMrP3A2e7+3+19hl3f5I4EdySU/e40r2h4BcRKWhvV8/twDVALYC7LyRG9pQGBb+ISEF7g38fd39mp211nV1MahT8IiIF7Q3+dWZ2KMkIHjP7P8Qi7KVBwS8iUtDeC7i+CEwHjjSzN4GlxEif0qDgFxEp2JNRPePNbF/ir4StwAXAshRr6zwKfhGRgja7esysn5ldY2Y/TJZcfIcYe78EmNjWZ4uKgl9EpGB3Lf67gA3AXOBzwNeAHsC57r4g3dI6kYJfRKRgd8F/iLsfA2BmPwHWAcOT2TZLh4JfRKRgd6N6ahsfuHs9sLTkQh+grk7BLyKS2F2L/1gza5xR04DeyXMD3N37pVpdZ1GLX0SkoM3gd/fySMv6ei20LiKSyMeSVGrxi4gUKPhFRHJGwS8ikjMKfhGRnEkt+M3sDjNba2aLmmybamZvmtmC5HZWWvtvRsEvIlKQZov/f4AJLWy/xd1HJ7cHUtz/Dgp+EZGC1ILf3R8H3krr5+8RBb+ISEEWffyXm9nCpCuof2tvMrNJZjbPzObV1NTs3R4V/CIiBV0d/LcChwKjiYVcbmrtje4+3d2r3b26qqpq7/aq4BcRKejS4Hf3Ne5e7+4NxDq+Y7pkxwp+EZGCLg1+MxvS5Ol5wKLW3tupFPwiIgWpTWBjZncD44BBZrYCuBYYZ2ajibV7Xwc+n9b+m1Hwi4gUpBb87n5RC5tnpLW/Nin4RUQKdOWuiEjOKPhFRHJGwS8ikjMKfhGRnMlH8NfVQffuWVchIlIU8hP8WnpRRARQ8IuI5E4+gr+2VsEvIpLIR/Crj19EpKD8g7+hAdzV4hcRSZR/8NfVxb2CX0QEyEPw19bGvYJfRATIQ/CrxS8i0kx+gl8nd0VEgDwFv1r8IiJAisGfLKa+1swWNdk2wMzmmNkryX2ri613GvXxi4g0k2aL/3+ACTttmww87O4jgYeT5+lSi19EpJnUgt/dHwfe2mnzOcDM5PFM4Ny09l+gPn4RkWa6uo9/sLuvAkjuD2jtjWY2yczmmdm8mpqaju9RLX4RkWaK9uSuu09392p3r66qqur4D1Lwi4g009XBv8bMhgAk92tT36NO7oqINNPVwT8buDh5fDFwf+p7VB+/iEgzaQ7nvBuYCxxhZivM7FJgGnCamb0CnJY8T5e6ekREmkktDd39olZeOjWtfbZIwS8i0kzRntztNOrjFxFppvyDXy1+EZFm8hP8OrkrIgLkKfjV4hcRAfIQ/OrjFxFppvyDXy1+EZFm8hP86uMXEQHyFPxq8YuIAAp+EZHcKf/g18ldEZFmyj/41eIXEWkmP8Gvk7siIkCegl8tfhERIA/Brz5+EZFmyj/41eIXEWkmkzQ0s9eBzUA9UOfu1antrDH4KytT24WISCnJshn8v9x9Xep7qauL1r5Z6rsSESkF5d/VU1urbh4RkSayCn4H/mRm881sUktvMLNJZjbPzObV1NR0fE+NLX4REQGyC/6T3P144Ezgi2Z28s5vcPfp7l7t7tVVVVUd31Ndncbwi4g0kUnwu/vK5H4tcB8wJrWdqcUvItJMlwe/me1rZn0bHwOnA4tS26GCX0SkmSwScTBwn8Uom27AL9z9j6ntTSd3RUSa6fJEdPfXgGO7bIdq8YuINFP+wzl1cldEpJl8BL9a/CIiBeUf/OrjFxFppvyDXy1+EZFm8hH86uMXESnIR/CrxS8iUlD+wb9tG/TokXUVIiJFo/yDf+NG2H//rKsQESka5R/8GzZA//5ZVyEiUjQU/CIiOVPewf/uu7B1q4JfRKSJ8g7+DRviXsEvIlKg4BcRyRkFv4hIzij4RURyJpPgN7MJZvaSmS0xs8mp7UjBLyKyiyyWXqwEfkQstH4UcJGZHZXKzhT8IiK7yKLFPwZY4u6vuft24JfAOansqTH4deWuiEhBFsF/EPBGk+crkm2db8MG6NNHs3OKiDSRRfBbC9t8lzeZTTKzeWY2r6ampmN7GjUKJk7s2GdFRMpUFsG/AhjW5PlQYOXOb3L36e5e7e7VVVVVHdvTpZfCjBkd+6yISJnKIvifBUaa2cFm1gO4EJidQR0iIrnU5SuUuHudmV0OPARUAne4+4tdXYeISF5lsjSVuz8APJDFvkVE8q68r9wVEZFdKPhFRHJGwS8ikjMKfhGRnFHwi4jkjLnvctFs0TGzGmBZBz8+CFjXieWkRXV2rlKosxRqBNXZ2bqyzve6+y5XwJZE8O8NM5vn7tVZ17E7qrNzlUKdpVAjqM7OVgx1qqtHRCRnFPwiIjmTh+CfnnUB7aQ6O1cp1FkKNYLq7GyZ11n2ffwiItJcHlr8IiLShIJfRCRnyjr4zWyCmb1kZkvMbHLW9TQys9fN7AUzW2Bm85JtA8xsjpm9ktx3+QrxZnaHma01s0VNtrVal5ldkxzbl8zsjIzrnGpmbybHdIGZnVUEdQ4zs0fMbLGZvWhmX062F80xbaPGojqeZtbLzJ4xs+eTOr+VbC+aY7mbOovqeOLuZXkj5vp/FTgE6AE8DxyVdV1Jba8Dg3badj0wOXk8GfhuBnWdDBwPLNpdXcBRyTHtCRycHOvKDOucCny1hfdmWecQ4PjkcV/g5aSeojmmbdRYVMeTWLK1T/K4O/A0MLaYjuVu6iyq41nOLf4xwBJ3f83dtwO/BM7JuKa2nAPMTB7PBM7t6gLc/XHgrZ02t1bXOcAv3f1dd18KLCGOeVZ1tibLOle5+3PJ483AYuAgiuiYtlFjazI5nh62JE+7JzeniI7lbupsTSZ1lnPwHwS80eT5Ctr+B92VHPiTmc03s0nJtsHuvgriPyNwQGbVNddaXcV4fC83s4VJV1Djn/xFUaeZjQCOI1qARXlMd6oRiux4mlmlmS0A1gJz3L0oj2UrdUIRHc9yDn5rYVuxjF09yd2PB84EvmhmJ2ddUAcU2/G9FTgUGA2sAm5Ktmdep5n1AX4DXOnum9p6awvbuqTWFmosuuPp7vXuPhoYCowxs1FtvL3Y6iyq41nOwb8CGNbk+VBgZUa1NOPuK5P7tcB9xJ92a8xsCEByvza7Cptpra6iOr7uvib5D9cA3M6OP5czrdPMuhOB+nN3vzfZXFTHtKUai/V4JrVtBB4FJlBkx7KppnUW2/Es5+B/FhhpZgebWQ/gQmB2xjVhZvuaWd/Gx8DpwCKitouTt10M3J9Nhbtora7ZwIVm1tPMDgZGAs9kUB9Q+E/f6DzimEKGdZqZATOAxe5+c5OXiuaYtlZjsR1PM6sys/2Tx72B8cA/KKJj2VadxXY8Uz1znPUNOIsYpfAq8PWs60lqOoQ4i/888GJjXcBA4GHgleR+QAa13U38GVpLtEQubasu4OvJsX0JODPjOu8CXgAWEv+ZhhRBnR8i/mxfCCxIbmcV0zFto8aiOp7A+4G/JfUsAv5vsr1ojuVu6iyq46kpG0REcqacu3pERKQFCn4RkZxR8IuI5IyCX0QkZxT8IiI5o+AX6SAz29/MvpB1HSJ7SsEv0nH7Awp+KTkKfpGOmwYcmsyvfkPWxYi0ly7gEumgZDbL37t7W5OFiRQdtfhFRHJGwS8ikjMKfpGO20wsVyhSUhT8Ih3k7uuBv5jZIp3clVKik7siIjmjFr+ISM4o+EVEckbBLyKSMwp+EZGcUfCLiOSMgl9EJGcU/CIiOfP/AX/gwwF9LsWVAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Standardized\n",
    "plt.figure(0)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"Regret\")\n",
    "plt.plot(np.cumsum(np.mean(opt - ts_rewards_per_experiment, axis=0))/np.std(opt - ts_rewards_per_experiment), 'r')\n",
    "plt.legend([\"TS\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Considering all the experiments:\n",
      "-----------------------------------------------\n",
      "Total expected reward over 365 days and its standard deviation considering 20 experiments\n",
      "42941.80120664478 39.93409041240419\n",
      "-----------------------------------------------\n",
      "Total expected regret over 365 days and its standard deviation considering 20 experiments\n",
      "324.1356666547668 39.93409041240343\n",
      "-----------------------------------------------\n",
      "Average expected reward per round over 365 days and its standard deviation between the rounds considering 20 experiments\n",
      "117.64877042916379 7.510649502171614\n",
      "-----------------------------------------------\n",
      "Average expected regret per round over 365 days and its standard deviation between the rounds considering 20 experiments\n",
      "0.8880429223418268 7.510649502171614\n"
     ]
    }
   ],
   "source": [
    "print(\"_______________________________________________\")\n",
    "print(\"Considering all the experiments:\")\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Total expected reward over\",n_days, \"days and its standard deviation considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.sum(ts_rewards_per_experiment, axis=1)),np.std(np.sum(ts_rewards_per_experiment, axis = 1)))\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Total expected regret over\",n_days, \"days and its standard deviation considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.sum(opt - ts_rewards_per_experiment, axis = 1)), np.std(np.sum(opt - ts_rewards_per_experiment, axis=1)))\n",
    "\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Average expected reward per round over\",n_days, \"days and its standard deviation between the rounds considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.mean(ts_rewards_per_experiment, axis=0)), np.std(np.mean(ts_rewards_per_experiment, axis=0)))\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Average expected regret per round over\",n_days, \"days and its standard deviation between the rounds considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.mean(opt-ts_rewards_per_experiment, axis=0)), np.std(np.mean(opt-ts_rewards_per_experiment, axis=0)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'Expected regret per round')"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1296x216 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (18,3))\n",
    "ax[0].plot((np.mean(ts_rewards_per_experiment, axis=0)), 'r')\n",
    "ax[0].set_title(\"Expected reward per round\")\n",
    "ax[1].plot((np.mean(opt-ts_rewards_per_experiment, axis=0)), 'r')\n",
    "ax[1].set_title(\"Expected regret per round\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Expected rewards per arm for the last experiment\n",
      "[[ 6.54348173  4.45499599  1.91128676  0.        ]\n",
      " [ 5.02579172  3.56032714  0.70576471  0.        ]\n",
      " [22.23857089 16.4292013   5.0589      0.        ]\n",
      " [44.77481459 38.48370901  7.45136842  0.        ]\n",
      " [39.89618278 34.77073139 21.47440079  3.88861111]]\n",
      "_______________________________________________\n",
      "Pulls per arm for the last experiment\n",
      "[358, 2, 1, 0]\n",
      "[359, 2, 0, 0]\n",
      "[358, 2, 1, 0]\n",
      "[358, 3, 0, 0]\n",
      "[354, 5, 2, 0]\n"
     ]
    }
   ],
   "source": [
    "#Considering one experiment to have an idea about expected rewards per arm and number of pulls per arm\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Expected rewards per arm for the last experiment\")    \n",
    "print(ts_learner.expected_rewards)\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Pulls per arm for the last experiment\")\n",
    "for i in range(5):\n",
    "    pulls_per_arm = [len(ts_learner.rewards_per_arm[i][0])-1,len(ts_learner.rewards_per_arm[i][1])-1,len(ts_learner.rewards_per_arm[i][2])-1,len(ts_learner.rewards_per_arm[i][3])-1]\n",
    "\n",
    "    print(pulls_per_arm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.special import rel_entr\n",
    "KL = sum(rel_entr([opt for i in range(n_days)],ts_rewards_per_day))\n",
    "#KL divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\foxfo\\AppData\\Local\\Temp\\ipykernel_20476\\1199476239.py:3: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  KL[i] = opt * np.log(opt/ts_rewards_per_day[i])\n"
     ]
    }
   ],
   "source": [
    "KL = np.zeros(n_days)\n",
    "for i in range(n_days):\n",
    "    KL[i] = opt * np.log(opt/ts_rewards_per_day[i]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1615.681946167589"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empiric_regret_ts = np.sum(opt-ts_rewards_per_day)\n",
    "empiric_regret_ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Upper bound for the TS regret\n",
      "700.7549269159446\n",
      "_______________________________________________\n",
      "Ratio between empirical regret and upper bound for the regret\n",
      "2.305630519471738\n"
     ]
    }
   ],
   "source": [
    "#Theoretical bounds for TS\n",
    "delta_ts = opt - ts_rewards_per_day\n",
    "UPPER_bound_regret_ts = (1+10)*np.log(ts_learner.t)+np.log(np.log(ts_learner.t))*np.sum(delta_ts/KL)\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Upper bound for the TS regret\")\n",
    "print(UPPER_bound_regret_ts)\n",
    "# ratio empiric_regret/upper_bound\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Ratio between empirical regret and upper bound for the regret\")\n",
    "print( empiric_regret_ts/UPPER_bound_regret_ts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## UCB: : optimization of the cumulative expected margin over all the products"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "#UCB\n",
    "n_arms = 4\n",
    "num_users = 100\n",
    "n_days = 365\n",
    "fixed_alpha = 1\n",
    "fixed_weights = 1\n",
    "fixed_units = 1\n",
    "n_experiments = 20\n",
    "\n",
    "ucb_rewards_per_experiment = []\n",
    "\n",
    "ucb_rewards_per_day_per_experiment = []\n",
    "ucb_rewards_per_day = np.zeros(n_days)\n",
    "\n",
    "for e in range(n_experiments):\n",
    "\n",
    "    env = Environment(n_arms, E, margins_matrix, num_users, fixed_alpha,fixed_weights, fixed_units)\n",
    "    ucb_learner = UCB(n_arms=n_arms)\n",
    "\n",
    "    for d in range(n_days):\n",
    "\n",
    "        pulled_arm = ucb_learner.pull_arm()\n",
    "        reward = env.round(pulled_arm)\n",
    "        ucb_learner.update(pulled_arm, reward)\n",
    "        ucb_rewards_per_day[d] += np.sum(reward)\n",
    "\n",
    "    ucb_rewards_per_experiment.append(ucb_learner.collected_rewards)\n",
    "\n",
    "ucb_rewards_per_day = ucb_rewards_per_day/n_experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"Regret\")\n",
    "plt.plot(np.cumsum(np.mean(opt - ucb_rewards_per_experiment, axis=0)), 'b')\n",
    "plt.legend([\"UCB\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Standardized\n",
    "plt.figure(0)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"Regret\")\n",
    "plt.plot(np.cumsum(np.mean(opt - ucb_rewards_per_experiment, axis=0)/np.std(opt - ucb_rewards_per_experiment)), 'b')\n",
    "plt.legend([\"UCB\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Considering all the experiments:\n",
      "-----------------------------------------------\n",
      "Total expected reward over 365 days and its standard deviation between 20 experiments\n",
      "47225.93142000001 401.2610716997115\n",
      "-----------------------------------------------\n",
      "Total expected regret over 365 days and its standard deviation between 20 experiments\n",
      "1758.1008061675893 401.2610716997117\n",
      "-----------------------------------------------\n",
      "Average expected reward per round over 365 days and its standard deviation between the rounds considering 20 experiments\n",
      "129.38611347945206 12.415303819960528\n",
      "-----------------------------------------------\n",
      "Average expected regret per round over 365 days and its standard deviation between the rounds considering 20 experiments\n",
      "4.81671453744545 12.415303819960526\n"
     ]
    }
   ],
   "source": [
    "print(\"_______________________________________________\")\n",
    "print(\"Considering all the experiments:\")\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Total expected reward over\",n_days, \"days and its standard deviation between\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.sum(ucb_rewards_per_experiment, axis=1)),np.std(np.sum(ucb_rewards_per_experiment, axis = 1)))\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Total expected regret over\",n_days, \"days and its standard deviation between\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.sum(opt - ucb_rewards_per_experiment, axis = 1)), np.std(np.sum(opt - ucb_rewards_per_experiment, axis=1)))\n",
    "\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Average expected reward per round over\",n_days, \"days and its standard deviation between the rounds considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.mean(ucb_rewards_per_experiment, axis=0)), np.std(np.mean(ucb_rewards_per_experiment, axis=0)))\n",
    "print(\"-----------------------------------------------\")\n",
    "print(\"Average expected regret per round over\",n_days, \"days and its standard deviation between the rounds considering\", n_experiments,\"experiments\")\n",
    "print(np.mean(np.mean(opt-ucb_rewards_per_experiment, axis=0)), np.std(np.mean(opt-ucb_rewards_per_experiment, axis=0)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Expected regret per round')"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (18,3))\n",
    "ax[0].plot((np.mean(ucb_rewards_per_experiment, axis=0)), 'b')\n",
    "ax[0].set_title(\"Expected reward per round\")\n",
    "ax[1].plot((np.mean(opt-ucb_rewards_per_experiment, axis=0)), 'b')\n",
    "ax[1].set_title(\"Expected regret per round\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Expected rewards per arm for the last experiment\n",
      "[[ 7.996       9.34204624  0.          0.        ]\n",
      " [ 5.93045495  6.69738947  0.          0.        ]\n",
      " [23.32584401  0.          0.          0.        ]\n",
      " [46.40052174 40.30931429 17.697      26.596     ]\n",
      " [39.995      45.52809278 17.14142857  0.        ]]\n",
      "_______________________________________________\n",
      "Pulls per arm for the last experiment\n",
      "[50, 309, 1, 1]\n",
      "[73, 284, 1, 3]\n",
      "[358, 1, 1, 1]\n",
      "[321, 34, 1, 5]\n",
      "[64, 290, 6, 1]\n",
      "_______________________________________________\n",
      "Upper confidence bounds for the last experiment\n",
      "[[0.48261976 0.19541504 1.9727697  2.03933398]\n",
      " [0.40176474 0.20383467 1.9727697  1.84823591]\n",
      " [0.18154977 1.89301847 1.9727697  2.03933398]\n",
      " [0.19172763 0.57751399 1.9727697  1.34649166]\n",
      " [0.41785347 0.20171501 1.29150381 2.03933398]]\n"
     ]
    }
   ],
   "source": [
    "#Considering one experiment to have an idea about expected rewards per arm and number of pulls per arm\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Expected rewards per arm for the last experiment\")    \n",
    "print(ucb_learner.expected_rewards)\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Pulls per arm for the last experiment\")\n",
    "for i in range(5):\n",
    "    pulls_per_arm = [len(ucb_learner.rewards_per_arm[i][0])-1,len(ucb_learner.rewards_per_arm[i][1])-1,len(ucb_learner.rewards_per_arm[i][2])-1,len(ucb_learner.rewards_per_arm[i][3])-1]\n",
    "\n",
    "    print(pulls_per_arm)\n",
    "\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Upper confidence bounds for the last experiment\")\n",
    "print(ucb_learner.confidence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Upper bound theoretical regret per product\n",
      "[ 85.75672853 156.25716978 213.58526483   0.         622.08398896]\n",
      "Ratio between empiric regret and the upper bound\n",
      "1.6313707815998468\n"
     ]
    }
   ],
   "source": [
    "#Theoretical comparison (?)\n",
    "\n",
    "opt_per_product = np.zeros(5)\n",
    "delta_arms_per_product = np.zeros((5,4)) #differencees with the mean reward of the optimal arm\n",
    "upper_bound_regret_per_product = np.zeros(5)\n",
    "for i in range(5):\n",
    "    opt_per_product[i] = np.max(margins_matrix[i,:] * conversion_rates[i])\n",
    "    for j in range(4):\n",
    "        delta_arms_per_product[i,j] = opt_per_product[i] - ucb_learner.expected_rewards[i,j]\n",
    "        if delta_arms_per_product[i,j]>0:\n",
    "            upper_bound_regret_per_product[i] += 4*np.log(ucb_learner.t)/delta_arms_per_product[i,j] + 8*delta_arms_per_product[i,j]\n",
    "   \n",
    "\n",
    "#R(UCB)<SUM(4*np.log(ucb_learner.t)/delta_arms_per_product[i,j] + 8*delta_arms_per_product[i,j])\n",
    "print(\"Upper bound theoretical regret per product\")\n",
    "print(upper_bound_regret_per_product)\n",
    "print(\"Ratio between empiric regret and the upper bound\")\n",
    "empiric_regret = np.mean(np.sum(opt - ucb_rewards_per_experiment, axis = 1))\n",
    "print(empiric_regret/np.sum(upper_bound_regret_per_product))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_______________________________________________\n",
      "Upper bound for the UCB regret\n",
      "332808.4483831572\n",
      "_______________________________________________\n",
      "Ratio between empirical regret and upper bound for the regret\n",
      "0.005282620722847491\n"
     ]
    }
   ],
   "source": [
    "#Theoretical bounds for UCB\n",
    "delta_ucb = opt - ucb_rewards_per_day\n",
    "UPPER_bound_regret_ucb = 4*np.log(ucb_learner.t)*np.sum(1/delta_ucb+8*delta_ucb)\n",
    "empiric_regret_ucb = np.sum(opt-ucb_rewards_per_day)\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Upper bound for the UCB regret\")\n",
    "print(UPPER_bound_regret_ucb)\n",
    "# ratio empiric_regret/upper_bound\n",
    "print(\"_______________________________________________\")\n",
    "print(\"Ratio between empirical regret and upper bound for the regret\")\n",
    "print( empiric_regret_ucb/UPPER_bound_regret_ucb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Greedy Learner: each round chose the current best solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# (INUTILE)\n",
    "#Greedy Learner\n",
    "n_arms = 4\n",
    "\n",
    "num_users = 100\n",
    "n_days = 365\n",
    "fixed_alpha = 1\n",
    "fixed_weights = 1\n",
    "margins_matrix = np.array([[2.,  5.,  8., 11.], [4.,  7., 10., 13.],[6.,  9., 12., 15.],[ 8., 11., 14., 17],[10., 13., 16., 19.]])\n",
    "\n",
    "env = Environment(n_arms, E, margins_matrix, num_users, fixed_alpha, fixed_weights, fixed_units=1)\n",
    "gr_learner = Greedy(n_arms=n_arms)\n",
    "\n",
    "for d in range(n_days):\n",
    "    \n",
    "    pulled_arm = gr_learner.pull_arm(env.margins_matrix)\n",
    "    reward = env.round(pulled_arm)\n",
    "    gr_learner.update(pulled_arm, reward, env.clicks_current_day, env.purchases_current_day)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1bb2b3fba60>]"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.cumsum(opt-gr_learner.collected_rewards),'g')"
   ]
  }
 ],
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