allocation_binary_decision_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b60f21c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from cvxopt import matrix, solvers, log, exp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib\n",
    "plt.style.use('ggplot')\n",
    "matplotlib.rcParams.update({\"axes.grid\" : False})\n",
    "\n",
    "from PyomoSolver import PyomoSolver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c055c2ad",
   "metadata": {},
   "source": [
    "### set up problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0981d0e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 80\n",
    "M = 80\n",
    "T = 500\n",
    "\n",
    "# noise sub-gaussianity parameter\n",
    "eta = 1\n",
    "# maximum value of R\n",
    "max_R = 1\n",
    "\n",
    "R_true = np.random.beta(10, 10, size=(N, M))\n",
    "\n",
    "plt.hist(R_true.flatten(), bins=np.int32(np.sqrt(N * M)))\n",
    "plt.show()\n",
    "# _, s, _ = np.linalg.svd(R_true)\n",
    "# plt.yscale(\"log\")\n",
    "# plt.plot(s)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f6eca7",
   "metadata": {},
   "source": [
    "### set static capacities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3ed84059",
   "metadata": {},
   "outputs": [],
   "source": [
    "# capacities\n",
    "C = np.ones(M)\n",
    "# demands\n",
    "D = np.ones(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7617babe",
   "metadata": {},
   "source": [
    "### ILP Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c1b7931f",
   "metadata": {},
   "outputs": [],
   "source": [
    "solver = PyomoSolver(N, M, C, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "331a61c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def shift_prices(R, x, p):\n",
    "    p_extended = np.tile(p,(N, 1))\n",
    "    margin = x * (R - p_extended) + (1 - x) * max_R\n",
    "    min_margin = np.min(margin)\n",
    "    return p + np.maximum(min_margin, 0) - 1e-15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "39519467",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_offerings_and_prices(R):\n",
    "    x = solver.solve_system(R)\n",
    "    p = solver.get_prices()\n",
    "    p = p - 1e-6\n",
    "    return x, p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a26a928",
   "metadata": {},
   "outputs": [],
   "source": [
    "def filter_decisions(x, p):\n",
    "    accepted = np.int32(R_true >= p)\n",
    "    x_accepted = x * accepted\n",
    "    # print(np.sum((R_true - p) * x, axis = 0))\n",
    "    return x_accepted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cfbb3d89",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_surplus(x):\n",
    "    return np.sum(x * R_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ba4fbcfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_dissatisfaction(x, p):\n",
    "    current_surplus = np.sum(x * (R_true - p), axis = 1)\n",
    "    best_surplus = np.maximum(np.max(R_true - p, axis = 1), 0)\n",
    "    return np.sum(best_surplus - current_surplus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "881e8398",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_proxy(R_lower, R_upper, alpha):\n",
    "    R_proxy = R_lower + alpha * (R_upper - R_lower)\n",
    "    return R_proxy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "979eb56e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_intervals(R_lower, R_upper, p, x_accepted, x_rejected):\n",
    "    p_extended = np.tile(p,(N, 1))\n",
    "    R_lower = np.maximum(R_lower, x_accepted * p_extended + (1 - x_accepted) * R_lower)\n",
    "    R_upper = np.minimum(R_upper, x_rejected * p_extended + (1 - x_rejected) * R_upper)\n",
    "    return R_lower, R_upper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee4516c7",
   "metadata": {},
   "source": [
    "### get the optimum solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "44637fe9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59.51160077483153\n",
      "[0.65511816 0.7057219  0.66871938 0.66007618 0.68464397 0.7451513\n",
      " 0.62739321 0.67849788 0.70528901 0.6469852  0.67180522 0.64457521\n",
      " 0.72262493 0.67785773 0.61283717 0.67685489 0.66648586 0.69287466\n",
      " 0.63590132 0.61818063 0.65144643 0.64891511 0.68051051 0.63535262\n",
      " 0.66467217 0.62924996 0.65506486 0.61822549 0.67604817 0.68948605\n",
      " 0.65730733 0.65823345 0.73320278 0.66389042 0.65865305 0.67303421\n",
      " 0.61718921 0.67441499 0.68358757 0.70198488 0.72296033 0.68723134\n",
      " 0.65998796 0.64986109 0.63722874 0.67379495 0.67195397 0.67119698\n",
      " 0.65058897 0.61216491 0.67874684 0.57500996 0.66099536 0.70896426\n",
      " 0.74312224 0.61405497 0.67136212 0.66168307 0.63694424 0.64939408\n",
      " 0.63891548 0.68261774 0.73586117 0.67300931 0.62960755 0.63331836\n",
      " 0.65884762 0.66691282 0.63023019 0.67495853 0.69520792 0.6755698\n",
      " 0.682439   0.62381427 0.73391724 0.65099201 0.67152547 0.73425625\n",
      " 0.69257126 0.68525333]\n"
     ]
    }
   ],
   "source": [
    "x_opt, p_opt = get_offerings_and_prices(R_true)\n",
    "surplus_opt = get_surplus(x_opt)\n",
    "print(surplus_opt)\n",
    "print(p_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72a944b7",
   "metadata": {},
   "source": [
    "### set the experiment history arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5ca4e186",
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_names = [\"LAC\", \"UCB with halving\", \"UCB with lower prices\", \"UCB with incremental prices\"]\n",
    "num_of_exp = len(exp_names)\n",
    "\n",
    "rewards = np.zeros((num_of_exp, T))\n",
    "acceptance = np.zeros((num_of_exp, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b52adab8",
   "metadata": {},
   "source": [
    "### learn-and-commit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "eabfffbc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.352958076798586e-10\n"
     ]
    }
   ],
   "source": [
    "R_true_flat = R_true.flatten()\n",
    "R_true_flat = np.sort(R_true_flat)\n",
    "R_diff = np.abs(np.diff(R_true_flat))\n",
    "print(np.min(R_diff))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e62184ba",
   "metadata": {},
   "source": [
    "#### duration estimate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ba6f11d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(395.5847207202499, 2463.9155676039773)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(N, M) * np.log2(np.log2(1/np.min(R_diff))), np.maximum(N, M) * np.log2(1/np.min(R_diff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d46933dc",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 27.35297804861599 16.885324757252242 0.5875\n",
      "10 22.97927215084014 17.25903065502809 0.4875\n",
      "20 22.327685343163076 17.410617462705158 0.475\n",
      "30 19.73250679115779 18.005796014710448 0.425\n",
      "40 17.789497465366242 17.94880534050199 0.375\n",
      "50 28.442331977040993 16.29597082882724 0.6\n",
      "60 20.01208846050971 17.72621434535852 0.425\n",
      "70 27.6341609859409 16.604141819927335 0.5875\n",
      "80 13.635942317861328 32.813814614192665 0.4\n",
      "90 18.22229013184468 31.498611378620808 0.525\n",
      "100 17.62869246544789 32.01588231019651 0.525\n",
      "110 18.9306805100941 31.59673111958959 0.5625\n",
      "120 20.100897721544197 32.1051185473314 0.625\n",
      "130 15.878540560577578 32.84883964375348 0.45\n",
      "140 19.223184623462743 32.19839649847154 0.575\n",
      "150 13.302475618100793 33.81448680181036 0.4125\n",
      "160 19.668706681618314 31.032603804332005 0.4875\n",
      "170 21.136148684348164 25.959752826117324 0.5375\n",
      "180 20.462130072719454 26.057444702924954 0.5125\n",
      "190 21.88087471714691 29.698985012770386 0.575\n",
      "200 18.6548148918295 27.0512013770461 0.475\n",
      "210 14.771856773938772 25.955523430392287 0.35\n",
      "220 21.37054372774932 31.357558931153484 0.5625\n",
      "230 13.871245641210983 32.437374304788136 0.35\n",
      "240 20.981114428237642 29.598552031529792 0.5\n",
      "250 21.484471811775606 26.805641030680462 0.525\n",
      "260 25.056688472350267 27.35048390419889 0.6\n",
      "270 19.76290133953625 29.18562255936643 0.5125\n",
      "280 24.544478495786514 29.859575015884346 0.6375\n",
      "290 15.685796158069529 28.75053335897697 0.4125\n",
      "300 15.946330031818066 30.579026755577242 0.4125\n",
      "310 21.995696337445455 31.298010853949716 0.5375\n",
      "320 18.81940784224089 28.931842784397258 0.4625\n",
      "330 21.266980757863088 27.761008311714242 0.525\n",
      "340 17.60006015809477 28.41333390371915 0.425\n",
      "350 18.169202482656864 29.168920809445325 0.4625\n",
      "360 20.048226353140052 30.704559464341838 0.525\n",
      "370 22.294649875534933 28.65097590014458 0.5375\n",
      "380 16.92257719063651 30.189715906919343 0.4375\n",
      "390 18.309508305757713 30.60253692589486 0.45\n",
      "400 18.857609720796816 28.777278710277145 0.45\n",
      "410 17.51749705496735 28.024123292425386 0.4375\n",
      "420 20.3144642134097 29.22993104140268 0.5125\n",
      "430 18.087106952026645 28.98527164205035 0.4625\n",
      "440 18.41526075828918 30.92604501039789 0.4625\n",
      "450 21.469553547116114 28.895731163992306 0.5\n",
      "460 22.607754996177913 30.711884851805795 0.575\n",
      "470 21.29981214752192 31.202987304653156 0.5375\n",
      "480 21.29610429355325 29.180899165649443 0.525\n",
      "490 16.8993878448366 28.04470239392093 0.4125\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 0\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "#counts = np.ones((N, M))\n",
    "for t in range(T):\n",
    "        \n",
    "    # get a point in each interval\n",
    "    R_length = R_upper - R_lower\n",
    "    \n",
    "    if np.max(R_length) > delta:\n",
    "        x_offered, _ = get_offerings_and_prices(R_length)\n",
    "        p = np.max(get_proxy(R_lower, R_upper, 0.5) * x_offered, axis = 0)\n",
    "    else:\n",
    "        R_proxy = get_proxy(R_lower, R_upper, 0.5)\n",
    "        x_offered, p = get_offerings_and_prices(R_proxy)\n",
    "                    \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "\n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "        # print(to_learn)\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8e48eab",
   "metadata": {},
   "source": [
    "### UCB with halving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "82db74ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# def update_counts(counts, x_offered):\n",
    "#     new_counts = x_offered + (counts + 1) * (1 - x_offered)\n",
    "#     return new_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d93b5065",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 27.35297804861599 16.885324757252242 0.5875\n",
      "10 16.95433840622782 17.68926274796742 0.375\n",
      "20 17.99758050650625 17.08214473138029 0.375\n",
      "30 15.812255739504076 15.965032485824334 0.3125\n",
      "40 21.553650293581377 16.828331390158656 0.4625\n",
      "50 17.555267975629878 16.74490334897685 0.3625\n",
      "60 18.380454125729766 17.088414069660846 0.3875\n",
      "70 16.365510361384747 16.446092003182265 0.3375\n",
      "80 16.716605520561234 17.665113960016875 0.3625\n",
      "90 17.266197291955407 17.357738985456535 0.3625\n",
      "100 19.029227989482195 17.105157081019968 0.4\n",
      "110 13.822568272119995 17.603674755252413 0.3\n",
      "120 10.144502348833209 15.71053878586509 0.2\n",
      "130 18.205642457538623 7.9540136092435105 0.3125\n",
      "140 27.987227733598992 5.884378464088346 0.475\n",
      "150 28.405877119751594 6.36090645055628 0.475\n",
      "160 24.059755081615364 5.864643640167882 0.4\n",
      "170 37.184067016316064 4.364714951349015 0.625\n",
      "180 37.45143071582541 3.397702457004174 0.625\n",
      "190 52.33709604469601 1.7306165680700363 0.875\n",
      "200 52.313917530818884 1.206871351242338 0.875\n",
      "210 57.93211276981984 1.0131726057189012 0.975\n",
      "220 56.519085425556916 0.7293184495077433 0.95\n",
      "230 58.850004450081194 0.07382018724150652 0.9875\n",
      "240 59.51160077483153 0.05555722606822033 1.0\n",
      "250 59.51160077483153 0.05558160436793347 1.0\n",
      "260 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "270 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "280 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "290 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "300 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "310 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "320 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "330 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "340 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "350 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "360 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "370 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "380 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "390 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "400 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "410 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "420 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "430 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "440 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "450 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "460 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "470 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "480 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "490 59.51160077483153 1.0757990831500308e-07 1.0\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 1\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "\n",
    "for t in range(T):\n",
    "        \n",
    "    # get a point in each interval\n",
    "    R_proxy = get_proxy(R_lower, R_upper, 1)\n",
    "    x_offered, p_w = get_offerings_and_prices(R_proxy)\n",
    "    \n",
    "    p_learn = np.max(get_proxy(R_lower, R_upper, 0.5) * x_offered, axis = 0)\n",
    "        \n",
    "    R_length = R_upper - R_lower\n",
    "    to_learn = np.max(x_offered * (R_length > delta), axis = 0) > 0\n",
    "    p = to_learn * p_learn + (1 - to_learn) * p_w\n",
    "         \n",
    "#     p = np.minimum(p_learn, p_w)\n",
    "    \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "\n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "        # print(to_learn)\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dc60827",
   "metadata": {},
   "source": [
    "### UCB with lower price ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e5f1df08",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 38.62110229440606 18.91720051146217 0.9\n",
      "10 22.857382212798107 22.240034546287585 0.525\n",
      "20 24.794982236041548 22.473561765917992 0.575\n",
      "30 24.505731621478684 22.19953086578648 0.5375\n",
      "40 21.665404373353354 21.49661356972483 0.5\n",
      "50 25.246855493162506 21.78620292125241 0.5875\n",
      "60 20.35041300409506 22.611264952615848 0.45\n",
      "70 20.897811558032288 22.641960647612002 0.4875\n",
      "80 23.141910935931318 20.92419316265653 0.5125\n",
      "90 22.43274422507189 21.32237499245133 0.5\n",
      "100 22.750321699638278 21.878442413321153 0.5\n",
      "110 21.489931200344184 21.709738075767675 0.475\n",
      "120 21.30988525640847 23.025056861953157 0.5\n",
      "130 22.591525371408586 21.931096447270313 0.5\n",
      "140 17.07630736001348 21.122456475446477 0.375\n",
      "150 15.984747899977469 20.57297089163262 0.325\n",
      "160 23.491974650523687 12.457655586026313 0.4\n",
      "170 24.53764368258089 5.135535441408942 0.425\n",
      "180 41.112326667215164 3.700558770121078 0.6875\n",
      "190 41.98814017908384 2.8415712846465633 0.7\n",
      "200 53.925648054972854 0.7221955385295361 0.9\n",
      "210 54.27174829992813 0.7440852779907471 0.9125\n",
      "220 57.41636781419602 0.3143089156194643 0.9625\n",
      "230 59.51160077483153 9.572249548561729e-08 1.0\n",
      "240 59.51160077483153 9.572249548561729e-08 1.0\n",
      "250 59.51160077483153 9.572249548561729e-08 1.0\n",
      "260 59.51160077483153 9.572249548561729e-08 1.0\n",
      "270 59.51160077483153 9.572249548561729e-08 1.0\n",
      "280 59.51160077483153 9.572249548561729e-08 1.0\n",
      "290 59.51160077483153 9.572249548561729e-08 1.0\n",
      "300 59.51160077483153 9.572249548561729e-08 1.0\n",
      "310 59.51160077483153 9.572249548561729e-08 1.0\n",
      "320 59.51160077483153 9.572249548561729e-08 1.0\n",
      "330 59.51160077483153 9.572249548561729e-08 1.0\n",
      "340 59.51160077483153 9.572249548561729e-08 1.0\n",
      "350 59.51160077483153 9.572249548561729e-08 1.0\n",
      "360 59.51160077483153 9.572249548561729e-08 1.0\n",
      "370 59.51160077483153 9.572249548561729e-08 1.0\n",
      "380 59.51160077483153 9.572249548561729e-08 1.0\n",
      "390 59.51160077483153 9.572249548561729e-08 1.0\n",
      "400 59.51160077483153 9.572249548561729e-08 1.0\n",
      "410 59.51160077483153 9.572249548561729e-08 1.0\n",
      "420 59.51160077483153 9.572249548561729e-08 1.0\n",
      "430 59.51160077483153 9.572249548561729e-08 1.0\n",
      "440 59.51160077483153 9.572249548561729e-08 1.0\n",
      "450 59.51160077483153 9.572249548561729e-08 1.0\n",
      "460 59.51160077483153 9.572249548561729e-08 1.0\n",
      "470 59.51160077483153 9.572249548561729e-08 1.0\n",
      "480 59.51160077483153 9.572249548561729e-08 1.0\n",
      "490 59.51160077483153 9.572249548561729e-08 1.0\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 2\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "\n",
    "for t in range(T):\n",
    "        \n",
    "    # get a point in each interval\n",
    "    R_proxy = get_proxy(R_lower, R_upper, 1)\n",
    "    x_offered, p_w = get_offerings_and_prices(R_proxy)\n",
    "    \n",
    "    p_learn = np.max(get_proxy(R_lower, R_upper, 0.4) * x_offered, axis = 0)\n",
    "        \n",
    "    R_length = R_upper - R_lower\n",
    "    to_learn = np.max(x_offered * (R_length > delta), axis = 0) > 0\n",
    "    p = to_learn * p_learn + (1 - to_learn) * p_w\n",
    "         \n",
    "#     p = np.minimum(p_learn, p_w)\n",
    "    \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "\n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "        # print(to_learn)\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d642a6c",
   "metadata": {},
   "source": [
    "### UCB with incremental search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "946781d5",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 27.35297804861599 16.885324757252242 0.5875\n",
      "10 16.95433840622782 17.68926274796742 0.375\n",
      "20 18.47886261261059 16.971518375340438 0.3875\n",
      "30 20.18936752688506 16.949675694971553 0.425\n",
      "40 14.025223095205668 17.68674260395349 0.3\n",
      "50 13.831068242550694 17.469049026691945 0.2875\n",
      "60 20.293259627696898 16.655154239046013 0.425\n",
      "70 16.312269441549464 17.555493724737595 0.35\n",
      "80 14.47158001508863 17.235774370959344 0.3125\n",
      "90 14.136986418251563 17.603363094286472 0.3\n",
      "100 9.20217539399468 17.63722702851722 0.2\n",
      "110 11.030771840584414 17.421900370009183 0.225\n",
      "120 17.74545651394289 15.738108467307768 0.35\n",
      "130 40.59087683391782 10.21067573363797 0.7\n",
      "140 45.52891803439503 8.129695315428242 0.775\n",
      "150 48.12838271281437 6.224753946928736 0.8125\n",
      "160 51.36632669509001 5.1275747918492804 0.875\n",
      "170 52.654398256260336 3.9008605175071214 0.8875\n",
      "180 57.53965531202104 2.2049808794746517 0.975\n",
      "190 55.46904352018386 2.538535109102318 0.9375\n",
      "200 57.84766351803948 2.561895602514955 0.9875\n",
      "210 56.99168049487314 1.4114298001241727 0.9625\n",
      "220 56.8798382894673 1.3316460582891259 0.9625\n",
      "230 58.26758360124714 1.1268054724397705 0.9875\n",
      "240 58.95911129316384 1.1347769776567382 1.0\n",
      "250 58.95911129316384 1.1266633018754884 1.0\n",
      "260 58.95911129316384 1.1263581260942384 1.0\n",
      "270 58.95911129316384 1.1260529503129884 1.0\n",
      "280 58.95911129316384 1.1257477745317384 1.0\n",
      "290 58.95911129316384 1.1254425987504884 1.0\n",
      "300 58.95911129316384 1.1251374229692384 1.0\n",
      "310 58.95911129316384 1.1248322471879884 1.0\n",
      "320 58.95911129316384 1.1245270714067384 1.0\n",
      "330 58.95911129316384 1.1242218956254884 1.0\n",
      "340 58.95911129316384 1.1239167198442384 1.0\n",
      "350 58.95911129316384 1.1236115440629884 1.0\n",
      "360 58.95911129316384 1.1233063682817384 1.0\n",
      "370 58.95911129316384 1.1230011925004884 1.0\n",
      "380 58.95911129316384 1.1226960167192384 1.0\n",
      "390 58.95911129316384 1.1707231082581258 1.0\n",
      "400 58.95911129316384 1.1707231036015129 1.0\n",
      "410 58.95911129316384 1.1707230989449 1.0\n",
      "420 58.95911129316384 1.1707230942882871 1.0\n",
      "430 58.95911129316384 1.1707230896316743 1.0\n",
      "440 58.95911129316384 1.1707230849750614 1.0\n",
      "450 58.95911129316384 1.1707230803184485 1.0\n",
      "460 58.95911129316384 1.1707230756618356 1.0\n",
      "470 58.95911129316384 1.1707230710052228 1.0\n",
      "480 58.95911129316384 1.17072306634861 1.0\n",
      "490 58.95911129316384 1.170723061691997 1.0\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 3\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "R_length = R_upper - R_lower\n",
    "\n",
    "beta = 0.5 * np.ones((N, M))\n",
    "\n",
    "for t in range(T):\n",
    "        \n",
    "    R_proxy = R_upper.copy()\n",
    "    x_offered, p_w = get_offerings_and_prices(R_proxy)\n",
    "    \n",
    "    p_learn = np.max((R_lower + beta) * x_offered, axis = 0)\n",
    "        \n",
    "#     to_learn = np.max(x_offered * (R_length > delta), axis = 0) > 0\n",
    "#     p = to_learn * p_learn + (1 - to_learn) * p_w\n",
    "         \n",
    "    p = np.minimum(p_learn, p_w)\n",
    "    \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    \n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "    R_length = R_upper - R_lower\n",
    "\n",
    "    # update beta (price increments)\n",
    "    betas_to_shrink = (beta + 1e-13) > R_length\n",
    "    beta = (beta**2) * betas_to_shrink + beta * (1 - betas_to_shrink)\n",
    "  \n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        # print(beta)\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "#         print(np.max(np.int32(x_offered * R_length / beta), axis = 0))\n",
    "        # print(to_learn)\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "206047fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(num_of_exp):\n",
    "    plt.plot(np.arange(T), rewards[i], label = exp_names[i])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0232c455",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(num_of_exp):\n",
    "    plt.plot(np.arange(T), np.cumsum(surplus_opt - rewards[i]), label = exp_names[i])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11eb646c",
   "metadata": {},
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}