analyze_results_comparisons.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Policy Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from binomial_cis import binom_ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tasks = [\"Symbol\\nUnderstanding\", \"Reasoning\", \"Human\\nRecognition\"]\n",
    "n_tasks = len(tasks)\n",
    "\n",
    "n_rollouts = np.array([50, 110, 30])\n",
    "vc1_successes = np.array([6, 12, 4])\n",
    "rt2_successes = np.array([40, 53, 16])\n",
    "\n",
    "\n",
    "# get mc estimates of success rates\n",
    "mc_vc1 = vc1_successes / n_rollouts\n",
    "mc_rt2 = rt2_successes / n_rollouts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve for Confidence Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Comuting upper confidence bound\n",
      "Comuting upper confidence bound\n",
      "Comuting upper confidence bound\n",
      "Comuting lower confidence bound\n",
      "Comuting lower confidence bound\n",
      "Comuting lower confidence bound\n"
     ]
    }
   ],
   "source": [
    "alpha = 1-np.sqrt(0.95) # miscoverage probability\n",
    "\n",
    "vc1_ubs = np.array([binom_ci(vc1_successes[i], n_rollouts[i], alpha, 'ub', randomized=True) for i in range(n_tasks)])\n",
    "rt2_lbs = np.array([binom_ci(rt2_successes[i], n_rollouts[i], alpha, 'lb', randomized=True) for i in range(n_tasks)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "\n",
    "fig = plt.figure(figsize = (4, 3))\n",
    " \n",
    "# creating the bar plot\n",
    "plt.bar(tasks, 1-rt2_lbs, color ='cornflowerblue', alpha=0.8, width = 0.6, bottom=rt2_lbs, label=\"RT-2\")\n",
    "plt.axhline(y=mc_rt2[0], xmin = 0.05, xmax = 0.25, linestyle=\"--\", color=\"black\") \n",
    "plt.axhline(y=mc_rt2[1], xmin = 0.4, xmax = 0.6, linestyle=\"--\", color=\"black\") \n",
    "plt.axhline(y=mc_rt2[2], xmin = 0.75, xmax = 0.95, linestyle=\"--\", color=\"black\") \n",
    "\n",
    "plt.bar(tasks, vc1_ubs, color ='mediumpurple', width = 0.6, label=\"VC-1\")\n",
    "plt.axhline(y=mc_vc1[0], xmin = 0.05, xmax = 0.25, linestyle=\"--\", color=\"black\") \n",
    "plt.axhline(y=mc_vc1[1], xmin = 0.4, xmax = 0.6, linestyle=\"--\", color=\"black\") \n",
    "plt.axhline(y=mc_vc1[2], xmin = 0.75, xmax = 0.95, linestyle=\"--\", color=\"black\") \n",
    "\n",
    "plt.ylim(0,1)\n",
    "plt.ylabel(\"Success Rate\", fontsize=12)\n",
    "plt.legend()\n",
    "plt.savefig(\"media/comparison.svg\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "stochastic_verification",
   "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": "3.9.18"
  }
 },
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