ciDifference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log Likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Discretely many importance weights and rewards; a logging policy $h$; two policies whose value difference is being estimated; lower bound on value difference given sample $\\{ (u_i, w_i, r_i) \\}$ drawn from $h$ is $$\n",
    "\\begin{alignat}{2}\n",
    "&\\!\\min_{Q \\succeq 0} &\\qquad& \\sum_{u, w, r} (u - w) Q_{u, w, r} r,\\label{eq:mleci}\\\\\n",
    "&\\text{subject to} &  & \\sum_{u, w, r} Q_{u, w, r} = 1, \\tag{$\\beta$} \\label{eq:mlesum} \\\\\n",
    "&                  &  & \\sum_{u, w, r} u Q_{u, w, r} = 1, \\tag{$\\gamma$} \\label{eq:mlesumu} \\\\\n",
    "&                  &  & \\sum_{u, w, r} w Q_{u, w, r} = 1, \\tag{$\\tau$} \\label{eq:mlesumw} \\\\\n",
    "&                  &  & \\sum_{n} \\log\\left(Q^{\\text{(mle)}}_{u_n, w_n, r_n}\\right) \\leq \\Delta + \\sum_{n} \\log\\left(Q_{u_n, w_n, r_n}\\right), \\tag{$\\kappa$}\n",
    "\\end{alignat}\n",
    "$$ Assume no duplicates and reduplicate at the end. Lagrangian dual $\\ldots$\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&L(\\beta, \\gamma, \\tau, \\kappa, Q) \\\\\n",
    "&=\\sum_{u, w, r} (u - w) Q_{u, w, r} r + \\beta \\left( -1 + \\sum_{u, w, r} Q_{u, w, r} \\right) + \\gamma \\left( -1 + \\sum_{u, w, r} u Q_{u, w, r} \\right) + \\tau \\left( -1 + \\sum_{u, w, r} w Q_{u, w, r} \\right) + \\kappa \\left( \\sum_{n} \\log(Q^{\\text{(mle)}}_{u_n, w_n, r_n}) - \\Delta - \\sum_{n}  \\log(Q_{u_n, w_n, r_n}) \\right) \\\\\n",
    "&= -\\beta - \\gamma - \\tau - \\kappa \\left( \\Delta - \\sum_{n} \\log\\left(Q^{\\text{(mle)}}_{u_n, w_n, r_n}\\right) \\right) + \\sum_{u,w,r} \\left( \\beta + \\gamma  u + \\tau w + \\left(u - w\\right) r\\right) Q_{u, w, r} - \\kappa c_{u,w,r} \\log\\left(Q_{u, w, r}\\right) \\\\\n",
    "&= -\\beta - \\gamma - \\tau - \\kappa \\phi + \\sum_{u,w,r} \\left( \\beta + \\gamma  u + \\tau w + \\left(u - w\\right) r\\right) Q_{u, w, r} - \\kappa c_{u,w,r} \\log\\left(Q_{u, w, r}\\right) \\\\\n",
    "\\end{aligned}\n",
    "$$ Unbounded unless $\\forall u, w, r: \\beta + \\gamma  u + \\tau w + \\left(u - w\\right) r \\geq 0$.  Continuing $\\ldots$ $$\n",
    "\\begin{aligned}\n",
    "Q^*_{u,w,r} &= \\frac{\\kappa}{\\beta + \\gamma  u + \\tau w + \\left(u - w\\right) r} & (c_{u,w,r} = 1) \\\\\n",
    "g(\\beta, \\gamma, \\tau, \\kappa) &= -\\beta - \\gamma - \\tau - \\kappa \\left( -N + N \\log \\kappa + \\phi \\right) + \\kappa \\sum_n \\log\\left( \\beta + \\gamma u_n + \\tau w_n + \\left(u_n - w_n\\right) r_n \\right) \\\\\n",
    "&\\doteq x - y \\kappa - N \\kappa \\log \\kappa \\\\\n",
    "y &\\doteq -N + \\phi - \\sum_n \\log\\left( \\beta + \\gamma u_n + \\tau w_n + \\left(u_n - w_n\\right) r_n \\right) \\\\\n",
    "\\kappa^* &= \\exp\\left(-1 - \\frac{y}{N}\\right) = \\exp\\left(-\\frac{\\phi}{N} + \\frac{1}{N} \\sum_n \\log\\left( \\beta + \\gamma u_n + \\tau w_n + \\left(u_n - w_n\\right) r_n \\right) \\right) \\\\\n",
    "g(\\beta, \\gamma, \\tau) &= x + N \\kappa^* \\\\\n",
    "&= -\\beta - \\gamma - \\tau + N \\exp\\left(-\\frac{\\phi}{N} + \\frac{1}{N} \\sum_n \\log\\left( \\beta + \\gamma u_n + \\tau w_n + \\left(u_n - w_n\\right) r_n \\right) \\right) \\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CR(-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Discretely many importance weights and rewards; a logging policy $h$; two policies whose value difference is being estimated; lower bound on value difference given sample $\\{ (u_i, w_i, r_i) \\}$ drawn from $h$ is $$\n",
    "\\begin{alignat}{2}\n",
    "&\\!\\min_{Q \\succeq 0} &\\qquad& \\sum_{u, w, r} (u - w) Q_{u, w, r} r,\\label{eq:crminustwoci}\\\\\n",
    "&\\text{subject to} &  & \\sum_{u, w, r} Q_{u, w, r} = 1, \\tag{$\\beta$} \\label{eq:crminustwosum} \\\\\n",
    "&                  &  & \\sum_{u, w, r} u Q_{u, w, r} = 1, \\tag{$\\gamma$} \\label{eq:crminustwosumu} \\\\\n",
    "&                  &  & \\sum_{u, w, r} w Q_{u, w, r} = 1, \\tag{$\\tau$} \\label{eq:crminustwosumw} \\\\\n",
    "&                  &  & \\sum_{n} \\left( \\left(N Q_{w_n,r_n}\\right)^2 - 1\\right) \\leq \\Delta + \\sum_{n} \\left(\\left(N Q^{\\text{(mle)}}_{w_n,r_n}\\right)^2 - 1\\right), \\tag{$\\kappa$}\n",
    "\\end{alignat}\n",
    "$$\n",
    "Assume no duplicates and reduplicate at the end. Lagrangian dual $\\ldots$\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&L(\\beta, \\gamma, \\tau, \\kappa, Q) \\\\\n",
    "&=\\sum_{u, w, r} (u - w) Q_{u, w, r} r + \\beta \\left( -1 + \\sum_{u, w, r} Q_{u, w, r} \\right) + \\gamma \\left( -1 + \\sum_{u, w, r} u Q_{u, w, r} \\right) + \\tau \\left( -1 + \\sum_{u, w, r} w Q_{u, w, r} \\right) + \\kappa \\left( \\sum_{n} \\left( \\left(N Q_{w_n,r_n}\\right)^2 - 1\\right) - \\Delta - \\sum_{n} \\left(\\left(N Q^{\\text{(mle)}}_{w_n,r_n}\\right)^2 - 1\\right) \\right) \\\\\n",
    "&= -\\beta - \\gamma - \\tau + \\kappa \\left( -\\Delta - \\sum_{n} \\left(\\left(N Q^{\\text{(mle)}}_{w_n,r_n}\\right)^2 - 1\\right) \\right) + \\sum_{u,w,r} \\left( \\beta + \\gamma u + \\tau w + \\left(u - w\\right) r\\right) Q_{u, w, r} + \\kappa c_{u,w,r} \\left( \\left(N Q_{w_n,r_n}\\right)^2 - 1\\right) \\\\\n",
    "&= -\\beta - \\gamma - \\tau + \\kappa \\left( 2 N \\phi \\right) + \\sum_{u,w,r} \\left( \\beta + \\gamma u + \\tau w + \\left(u - w\\right) r\\right) Q_{u, w, r} + \\kappa c_{u,w,r} \\left( \\left(N Q_{w_n,r_n}\\right)^2 - 1\\right) \\\\\n",
    "\\end{aligned}\n",
    "$$ which is unbounded unless $\\forall u, w, r: \\beta + \\gamma u + \\tau w + \\left(u - w\\right) r \\geq 0$ but in that case $Q = 0$ for observed data points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Empirical on augmented support"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can place all mass on the sample and discard the dual variable constraint.  We augment the support where the log-likelihood solution potentially places additional mass: at an extreme value of $(u_{\\text{fake}}, w_{\\text{fake}})$ associated with $r_{\\text{fake}} = r_{\\min}\\ \\mathtt{if}\\ u_{\\text{fake}} \\geq w_{\\text{fake}}\\ \\mathtt{else}\\ r_{\\max}$.  We can try all extrema.\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Q_{u,w,r} &= \\max\\left\\{0, -\\frac{\\beta + \\gamma u + \\tau w + \\left(u - w\\right) r}{2 (N+1)^2 \\kappa}\\right\\}\n",
    "\\end{aligned}\n",
    "$$ Allow signed measures and drop the $\\max$.  Substitute $\\kappa \\leftarrow \\frac{1}{2 (N+1)} \\kappa$ to get $$\n",
    "\\begin{aligned}\n",
    "Q_{u,w,r} &= -\\frac{\\beta + \\gamma u + \\tau w + \\left(u - w\\right) r}{(N+1) \\kappa} \\\\\n",
    "g(\\beta,\\gamma,\\tau,\\kappa) &= -\\beta - \\gamma - \\tau + \\kappa \\left( \\phi - \\frac{1}{2} \\right) - \\frac{1}{\\kappa} \\frac{1}{2} \\frac{1}{N+1}\\sum_{n \\cup \\text{fake}} \\left( \\beta + \\gamma u + \\tau w + \\left(u - w\\right) r\\right)^2 \\\\\n",
    "&= -\\frac{1}{2 \\kappa} \\overline{(u - w)^2 r^2} + \\kappa \\left( \\phi - \\frac{1}{2} \\right) - \n",
    "\\left(\\begin{matrix} 1 + \\frac{1}{\\kappa} \\overline{(u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{u (u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\left(\\begin{matrix} \\beta \\\\ \\gamma \\\\ \\tau \\end{matrix}\\right)\n",
    " +  \\frac{1}{2} \\left(\\begin{matrix} \\beta \\\\ \\gamma \\\\ \\tau \\end{matrix}\\right)^\\top \n",
    " \\frac{-1}{\\kappa}\n",
    "\\left(\n",
    "\\begin{matrix}\n",
    "1 & \\overline{u} & \\overline{w} \\\\ \n",
    "\\overline{u} & \\overline{u^2} & \\overline{u w} \\\\ \n",
    "\\overline{w} & \\overline{u w} & \\overline{w^2} \\\\ \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "\\left(\\begin{matrix} \\beta \\\\ \\gamma \\\\ \\tau \\end{matrix}\\right) \\\\\n",
    "\\left(\\begin{matrix} \\beta^* \\\\ \\gamma^* \\\\ \\tau^* \\end{matrix}\\right) &= -\\kappa  \n",
    "\\left(\n",
    "\\begin{matrix}\n",
    "1 & \\overline{u} & \\overline{w} \\\\ \n",
    "\\overline{u} & \\overline{u^2} & \\overline{u w} \\\\ \n",
    "\\overline{w} & \\overline{u w} & \\overline{w^2} \\\\ \n",
    "\\end{matrix}\n",
    "\\right)^{-1} \n",
    "\\left(\\begin{matrix} 1 + \\frac{1}{\\kappa} \\overline{(u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{u (u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{w (u - w) r} \\end{matrix}\\right) \\\\\n",
    "&= -\\kappa \\left(\n",
    "\\begin{matrix}\n",
    "1 & \\overline{u} & \\overline{w} \\\\ \n",
    "\\overline{u} & \\overline{u^2} & \\overline{u w} \\\\ \n",
    "\\overline{w} & \\overline{u w} & \\overline{w^2} \\\\ \n",
    "\\end{matrix}\n",
    "\\right)^{-1} 1 - \\left(\n",
    "\\begin{matrix}\n",
    "1 & \\overline{u} & \\overline{w} \\\\ \n",
    "\\overline{u} & \\overline{u^2} & \\overline{u w} \\\\ \n",
    "\\overline{w} & \\overline{u w} & \\overline{w^2} \\\\ \n",
    "\\end{matrix}\n",
    "\\right)^{-1} \\left(\\begin{matrix} \\overline{(u - w) r} \\\\ \n",
    "\\overline{u (u - w) r} \\\\ \n",
    "\\overline{w (u - w) r} \\end{matrix}\\right) \\\\\n",
    "&\\doteq -\\kappa \\vec{a} - \\vec{b} \\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "g(\\kappa) &= -\\frac{1}{2 \\kappa} \\overline{(u - w)^2 r^2}\n",
    "+ \\kappa \\left( \\phi - \\frac{1}{2} \\right) \n",
    "- \\frac{1}{2}\n",
    "\\left(\\begin{matrix} 1 + \\frac{1}{\\kappa} \\overline{(u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{u (u - w) r} \\\\ \n",
    "1 + \\frac{1}{\\kappa} \\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\left(\\begin{matrix} \\beta^* \\\\ \\gamma^* \\\\ \\tau^* \\end{matrix}\\right) \\\\\n",
    "&= \\frac{1}{2}\n",
    "\\left(\\begin{matrix} \\overline{(u - w) r} \\\\ \n",
    "\\overline{u (u - w) r} \\\\ \n",
    "\\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\vec{a} \n",
    "+ \\frac{1}{2} 1^\\top \\vec{b}\n",
    "+ \\frac{1}{2 \\kappa} \\left(\n",
    "\\left(\\begin{matrix} \\overline{(u - w) r} \\\\ \n",
    "\\overline{u (u - w) r} \\\\ \n",
    "\\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\vec{b}\n",
    "- \\overline{(u - w)^2 r^2}\n",
    "\\right)\n",
    "+ \\kappa \\left( \\phi - \\frac{1}{2} + \\frac{1}{2} 1^\\top \\vec{a}\\right) \n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "&\\doteq x + y \\frac{1}{2 \\kappa} + z \\kappa \\\\\n",
    "x &= \\frac{1}{2}\n",
    "\\left(\\begin{matrix} \\overline{(u - w) r} \\\\ \n",
    "\\overline{u (u - w) r} \\\\ \n",
    "\\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\vec{a} \n",
    "+ \\frac{1}{2} 1^\\top \\vec{b} = 1^\\top \\vec{b} \\\\\n",
    "y &= \\left(\\begin{matrix} \\overline{(u - w) r} \\\\ \n",
    "\\overline{u (u - w) r} \\\\ \n",
    "\\overline{w (u - w) r} \\end{matrix}\\right)^\\top \n",
    "\\vec{b} - \\overline{(u - w)^2 r^2} \\\\\n",
    "z &= \\phi - \\frac{1}{2} + \\frac{1}{2} 1^\\top \\vec{a} \\\\\n",
    "\\kappa^* &= \\sqrt{\\frac{y}{2 z}} & (y \\leq 0, z < 0) \\\\\n",
    "g^* &= x - \\sqrt{2 y z}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Comparison with baselines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "code_folding": [
     0,
     53
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****** CrMinus2 ******\n",
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      "(2031, {'cov': 0.9521, 'covstd': 0.0021, 'ubcov': 0.9749, 'lbcov': 0.9772, 'width': 0.2605, 'widthstd': 0.0023, 'widthlo': 0.1219, 'widthhi': 0.912, 'ub': 0.1369, 'lb': -0.1236})\n",
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      "(28943, {'cov': 0.988, 'covstd': 0.0011, 'ubcov': 0.9941, 'lbcov': 0.9939, 'width': 0.1528, 'widthstd': 0.0002, 'widthlo': 0.1112, 'widthhi': 0.1889, 'ub': 0.0714, 'lb': -0.0814})\n",
      "(70171, {'cov': 0.9739, 'covstd': 0.0016, 'ubcov': 0.9877, 'lbcov': 0.9862, 'width': 0.0924, 'widthstd': 0.0001, 'widthlo': 0.0696, 'widthhi': 0.1088, 'ub': 0.0491, 'lb': -0.0433})\n",
      "(170126, {'cov': 0.9625, 'covstd': 0.0019, 'ubcov': 0.9822, 'lbcov': 0.9803, 'width': 0.0565, 'widthstd': 0.0001, 'widthlo': 0.0439, 'widthhi': 0.0651, 'ub': 0.0244, 'lb': -0.0321})\n",
      "(412463, {'cov': 0.9602, 'covstd': 0.002, 'ubcov': 0.9797, 'lbcov': 0.9805, 'width': 0.0352, 'widthstd': 0.0, 'widthlo': 0.028, 'widthhi': 0.0399, 'ub': 0.0169, 'lb': -0.0183})\n",
      "(1000000, {'cov': 0.9528, 'covstd': 0.0021, 'ubcov': 0.975, 'lbcov': 0.9778, 'width': 0.0221, 'widthstd': 0.0, 'widthlo': 0.0177, 'widthhi': 0.0248, 'ub': 0.0096, 'lb': -0.0125})\n",
      "****** MLE ******\n",
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      "(346, {'cov': 0.9982, 'covstd': 0.0004, 'ubcov': 0.9989, 'lbcov': 0.9993, 'width': 0.5881, 'widthstd': 0.0017, 'widthlo': 0.3209, 'widthhi': 0.877, 'ub': 0.2913, 'lb': -0.2967})\n",
      "(838, {'cov': 0.9995, 'covstd': 0.0002, 'ubcov': 0.9997, 'lbcov': 0.9998, 'width': 0.504, 'widthstd': 0.0013, 'widthlo': 0.2855, 'widthhi': 0.7187, 'ub': 0.2537, 'lb': -0.2504})\n",
      "(2031, {'cov': 0.9968, 'covstd': 0.0006, 'ubcov': 0.9985, 'lbcov': 0.9983, 'width': 0.4416, 'widthstd': 0.0011, 'widthlo': 0.2118, 'widthhi': 0.6146, 'ub': 0.2266, 'lb': -0.215})\n",
      "(4924, {'cov': 0.9886, 'covstd': 0.0011, 'ubcov': 0.9939, 'lbcov': 0.9947, 'width': 0.3626, 'widthstd': 0.0013, 'widthlo': 0.1438, 'widthhi': 0.5331, 'ub': 0.1839, 'lb': -0.1787})\n",
      "(11938, {'cov': 0.9598, 'covstd': 0.002, 'ubcov': 0.9792, 'lbcov': 0.9806, 'width': 0.2383, 'widthstd': 0.0014, 'widthlo': 0.1043, 'widthhi': 0.471, 'ub': 0.1139, 'lb': -0.1244})\n",
      "(28943, {'cov': 0.936, 'covstd': 0.0024, 'ubcov': 0.9655, 'lbcov': 0.9705, 'width': 0.1253, 'widthstd': 0.0008, 'widthlo': 0.0747, 'widthhi': 0.3941, 'ub': 0.0576, 'lb': -0.0677})\n",
      "(70171, {'cov': 0.9328, 'covstd': 0.0025, 'ubcov': 0.967, 'lbcov': 0.9658, 'width': 0.0759, 'widthstd': 0.0002, 'widthlo': 0.0523, 'widthhi': 0.098, 'ub': 0.0408, 'lb': -0.035})\n",
      "(170126, {'cov': 0.9394, 'covstd': 0.0024, 'ubcov': 0.9707, 'lbcov': 0.9687, 'width': 0.0503, 'widthstd': 0.0001, 'widthlo': 0.0364, 'widthhi': 0.0614, 'ub': 0.0214, 'lb': -0.029})\n",
      "(412463, {'cov': 0.9486, 'covstd': 0.0022, 'ubcov': 0.9742, 'lbcov': 0.9744, 'width': 0.0328, 'widthstd': 0.0, 'widthlo': 0.0253, 'widthhi': 0.0384, 'ub': 0.0157, 'lb': -0.0171})\n",
      "(1000000, {'cov': 0.9428, 'covstd': 0.0023, 'ubcov': 0.9715, 'lbcov': 0.9713, 'width': 0.021, 'widthstd': 0.0, 'widthlo': 0.0166, 'widthhi': 0.0239, 'ub': 0.0091, 'lb': -0.0119})\n",
      "****** Asymptotic Gaussian ******\n",
      "(10, {'cov': 0.8245, 'covstd': 0.0038, 'ubcov': 0.8626, 'lbcov': 0.9619, 'width': 1.1506, 'widthstd': 0.0052, 'widthlo': 0.0, 'widthhi': 1.9204, 'ub': 0.535, 'lb': -0.6155})\n",
      "(25, {'cov': 0.9161, 'covstd': 0.0028, 'ubcov': 0.9356, 'lbcov': 0.9805, 'width': 0.945, 'widthstd': 0.0028, 'widthlo': 0.5095, 'widthhi': 1.3699, 'ub': 0.4649, 'lb': -0.4801})\n",
      "(59, {'cov': 0.9304, 'covstd': 0.0025, 'ubcov': 0.9505, 'lbcov': 0.9799, 'width': 0.6681, 'widthstd': 0.0019, 'widthlo': 0.3983, 'widthhi': 0.9108, 'ub': 0.3321, 'lb': -0.3359})\n",
      "(143, {'cov': 0.9376, 'covstd': 0.0024, 'ubcov': 0.962, 'lbcov': 0.9756, 'width': 0.4645, 'widthstd': 0.0025, 'widthlo': 0.2829, 'widthhi': 0.5828, 'ub': 0.2366, 'lb': -0.2279})\n",
      "(346, {'cov': 0.9316, 'covstd': 0.0025, 'ubcov': 0.9658, 'lbcov': 0.9658, 'width': 0.3597, 'widthstd': 0.0037, 'widthlo': 0.1867, 'widthhi': 0.3999, 'ub': 0.1798, 'lb': -0.1798})\n",
      "(838, {'cov': 0.9069, 'covstd': 0.0029, 'ubcov': 0.9549, 'lbcov': 0.952, 'width': 0.3389, 'widthstd': 0.0048, 'widthlo': 0.125, 'widthhi': 1.7893, 'ub': 0.1881, 'lb': -0.1508})\n",
      "(2031, {'cov': 0.8549, 'covstd': 0.0035, 'ubcov': 0.9319, 'lbcov': 0.923, 'width': 0.3723, 'widthstd': 0.0048, 'widthlo': 0.081, 'widthhi': 1.4807, 'ub': 0.2121, 'lb': -0.1602})\n",
      "(4924, {'cov': 0.8375, 'covstd': 0.0037, 'ubcov': 0.933, 'lbcov': 0.9045, 'width': 0.3425, 'widthstd': 0.0032, 'widthlo': 0.0549, 'widthhi': 0.8932, 'ub': 0.174, 'lb': -0.1685})\n",
      "(11938, {'cov': 0.8645, 'covstd': 0.0034, 'ubcov': 0.9585, 'lbcov': 0.906, 'width': 0.2665, 'widthstd': 0.0016, 'widthlo': 0.0411, 'widthhi': 0.5213, 'ub': 0.1284, 'lb': -0.1381})\n",
      "(28943, {'cov': 0.9106, 'covstd': 0.0029, 'ubcov': 0.9853, 'lbcov': 0.9253, 'width': 0.1861, 'widthstd': 0.0007, 'widthlo': 0.073, 'widthhi': 0.2966, 'ub': 0.0877, 'lb': -0.0984})\n",
      "(70171, {'cov': 0.9353, 'covstd': 0.0025, 'ubcov': 0.9862, 'lbcov': 0.9491, 'width': 0.1227, 'widthstd': 0.0003, 'widthlo': 0.0674, 'widthhi': 0.176, 'ub': 0.0644, 'lb': -0.0583})\n",
      "(170126, {'cov': 0.9461, 'covstd': 0.0023, 'ubcov': 0.986, 'lbcov': 0.9601, 'width': 0.0801, 'widthstd': 0.0002, 'widthlo': 0.0507, 'widthhi': 0.1077, 'ub': 0.0363, 'lb': -0.0438})\n",
      "(412463, {'cov': 0.9478, 'covstd': 0.0022, 'ubcov': 0.9802, 'lbcov': 0.9676, 'width': 0.0516, 'widthstd': 0.0001, 'widthlo': 0.0344, 'widthhi': 0.0667, 'ub': 0.0253, 'lb': -0.0263})\n",
      "(1000000, {'cov': 0.9469, 'covstd': 0.0022, 'ubcov': 0.9782, 'lbcov': 0.9687, 'width': 0.0332, 'widthstd': 0.0001, 'widthlo': 0.0226, 'widthhi': 0.0422, 'ub': 0.0152, 'lb': -0.018})\n"
     ]
    }
   ],
   "source": [
    "def produceresults(env, method, minexp=1, maxexp=6, numpts=15, ndataperpt=100):\n",
    "    from math import ceil\n",
    "    import numpy\n",
    "    \n",
    "    (umin, umax), (wmin, wmax) = env.range()\n",
    "\n",
    "    for ndata in map(ceil, numpy.logspace(minexp, maxexp, numpts)):\n",
    "        bounds=[]\n",
    "        for i in range(1, ndataperpt+1):\n",
    "            (utrue, wtrue, data) = env.sample(ndata)\n",
    "            deltatrue = utrue - wtrue\n",
    "\n",
    "            try:\n",
    "                ci = method(data=data, umin=umin, umax=umax, wmin=wmin, wmax=wmax, alpha=0.05)\n",
    "                assert numpy.isfinite(ci[0]) and numpy.isfinite(ci[1])\n",
    "            except:\n",
    "                from pprint import pformat\n",
    "                print('truevalue was {}'.format((utrue, wtrue, deltatrue)))\n",
    "                print('data was {}'.format(data))\n",
    "                print('umin, umax, wmin, wmax was {}'.format((umin, umax, wmin, wmax)))\n",
    "                print('ci was {}'.format(pformat(ci)))\n",
    "                raise\n",
    "                                                \n",
    "            bounds.append(\n",
    "                ( deltatrue,\n",
    "                  data,\n",
    "                  [ \n",
    "                      ci[0], 'n/a', ci[1]\n",
    "                  ]\n",
    "                )  \n",
    "            )\n",
    "            \n",
    "        uppers = [ d[2][2] for d in bounds ]\n",
    "        lowers = [ d[2][0] for d in bounds ]\n",
    "        upperbounded = [ 1 if d[0] <= d[2][2] else 0 for d in bounds ]\n",
    "        lowerbounded = [ 1 if d[2][0] <= d[0] else 0 for d in bounds ]\n",
    "        covered = [ 1 if u*l > 0 else 0 for (u, l) in zip(upperbounded, lowerbounded) ]\n",
    "        width = [ d[2][2] - d[2][0] for d in bounds ]    \n",
    "        yield (ndata,\n",
    "                { \n",
    "                    'cov': numpy.mean(covered),\n",
    "                    'covstd': numpy.std(covered, ddof=1) / numpy.sqrt(len(covered) - 1),\n",
    "                    'ubcov': numpy.mean(upperbounded),\n",
    "                    'lbcov': numpy.mean(lowerbounded),\n",
    "                    'width': numpy.mean(width),\n",
    "                    'widthstd': numpy.std(width, ddof=1) / numpy.sqrt(len(width) - 1),\n",
    "                    'widthlo': numpy.quantile(width, q=[0.05])[0],\n",
    "                    'widthhi': numpy.quantile(width, q=[0.95])[0],\n",
    "                    'ub': numpy.mean(uppers),\n",
    "                    'lb': numpy.mean(lowers),\n",
    "                },\n",
    "              )\n",
    "        \n",
    "class AsymptoticGaussian:\n",
    "    def interval(data, alpha, **kwargs):\n",
    "        from math import sqrt\n",
    "        from scipy.stats import norm  \n",
    "\n",
    "        scale = norm.ppf(1-alpha/2)\n",
    "\n",
    "        n = sum(c for c, _, _, _ in data)\n",
    "        tot = sum(c*(u-w)*r for c, u, w, r in data)\n",
    "        muhat = tot / n\n",
    "        totsq = sum(c*((u-w)*r - muhat)**2 for c, u, w, r in data)\n",
    "        sigmahat = sqrt(totsq) / n\n",
    "\n",
    "        return max(-1, muhat - scale*sigmahat), min(1, muhat + scale*sigmahat)\n",
    " \n",
    "from environments.DoubleControlledRangeVariance import DoubleControlledRangeVariance as DCRV\n",
    "import MLE.MLE\n",
    "from MLE.MLE import CrMinusTwo as CrMinusTwo\n",
    "\n",
    "def getenv(wmax):\n",
    "    usupport = [ 0, 4, 500 ]\n",
    "    wsupport = [ 0, 2, wmax ]\n",
    "    env = DCRV(seed=45, usupport=usupport, expusq=50, wsupport=wsupport, expwsq=100)\n",
    "    return env\n",
    "\n",
    "allres = []\n",
    "for (name, method) in [ \n",
    "                        ('CrMinus2', lambda data, **kwargs: CrMinusTwo.intervaldiff(datagen=lambda: data, raiseonerr=True, **kwargs)[0]),\n",
    "                        ('MLE', lambda data, **kwargs: MLE.MLE.cidifference(datagen=lambda: data, raiseonerr=True, **kwargs)[0]),\n",
    "                        ('Asymptotic Gaussian', lambda **kwargs: AsymptoticGaussian.interval(**kwargs)),\n",
    "                      ]:\n",
    "    print('****** {} ******'.format(name))\n",
    "    res = []\n",
    "    wmax = 1000\n",
    "    for zzz in produceresults(getenv(wmax), method, minexp=1, ndataperpt=10000, numpts=14):\n",
    "        res.append( (zzz[0] / wmax, zzz[1]) )\n",
    "        print('{}'.format(( zzz[0], { y: round(z, 4) for y, z in zzz[1].items() })), flush=True)\n",
    "    allres.append((name, res))\n",
    "    del wmax\n",
    "import pickle\n",
    "pickle.dump( allres, open( \"epsilongreedy_cidiff_allres.p\", \"wb\" ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "code_folding": [
     2
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "class FlassPlot:\n",
    "    from matplotlib import scale as mscale\n",
    "    \n",
    "    class ExpScale(mscale.ScaleBase):\n",
    "        from matplotlib import transforms as mtransforms\n",
    "\n",
    "        \"\"\"\n",
    "        Scales data in range -Infinity, 1 using log(1 - x)\n",
    "        \"\"\"\n",
    "\n",
    "        # The scale class must have a member ``name`` that defines the\n",
    "        # string used to select the scale.  For example,\n",
    "        # ``gca().set_yscale(\"mercator\")`` would be used to select this\n",
    "        # scale.\n",
    "        name = 'exp'\n",
    "\n",
    "        def __init__(self, axis, **kwargs):\n",
    "            \"\"\"\n",
    "            Any keyword arguments passed to ``set_xscale`` and\n",
    "            ``set_yscale`` will be passed along to the scale's\n",
    "            constructor.\n",
    "            \"\"\"\n",
    "            from matplotlib import scale as mscale\n",
    "            myscale = kwargs.pop(\"expscale\", 1.0)\n",
    "            mscale.ScaleBase.__init__(self, axis, **kwargs)\n",
    "            self.myscale = myscale\n",
    "\n",
    "        def get_transform(self):\n",
    "            \"\"\"\n",
    "            Override this method to return a new instance that does the\n",
    "            actual transformation of the data.\n",
    "            \"\"\"\n",
    "            return FlassPlot.ExpScale.ExpTransform(self.myscale)\n",
    "\n",
    "        def set_default_locators_and_formatters(self, axis):\n",
    "            \"\"\"\n",
    "            Override to set up the locators and formatters to use with the\n",
    "            scale.  This is only required if the scale requires custom\n",
    "            locators and formatters.  Writing custom locators and\n",
    "            formatters is rather outside the scope of this example, but\n",
    "            there are many helpful examples in ``ticker.py``.\n",
    "\n",
    "            In our case, the Mercator example uses a fixed locator from\n",
    "            -90 to 90 degrees and a custom formatter class to put convert\n",
    "            the radians to degrees and put a degree symbol after the\n",
    "            value::\n",
    "            \"\"\"\n",
    "\n",
    "            return axis\n",
    "\n",
    "        def limit_range_for_scale(self, vmin, vmax, minpos):\n",
    "            \"\"\"\n",
    "            Override to limit the bounds of the axis to the domain of the\n",
    "            transform.\n",
    "            \"\"\"\n",
    "            return vmin, vmax\n",
    "\n",
    "        class ExpTransform(mtransforms.Transform):\n",
    "            # There are two value members that must be defined.\n",
    "            # ``input_dims`` and ``output_dims`` specify number of input\n",
    "            # dimensions and output dimensions to the transformation.\n",
    "            # These are used by the transformation framework to do some\n",
    "            # error checking and prevent incompatible transformations from\n",
    "            # being connected together.  When defining transforms for a\n",
    "            # scale, which are, by definition, separable and have only one\n",
    "            # dimension, these members should always be set to 1.\n",
    "            input_dims = 1\n",
    "            output_dims = 1\n",
    "            is_separable = True\n",
    "\n",
    "            def __init__(self, scale):\n",
    "                from matplotlib import transforms as mtransforms\n",
    "                \n",
    "                mtransforms.Transform.__init__(self)\n",
    "                self.scale = scale\n",
    "\n",
    "            def transform_non_affine(self, a):\n",
    "                \"\"\"\n",
    "                This transform takes an Nx1 ``numpy`` array and returns a\n",
    "                transformed copy.  Since the range of the Mercator scale\n",
    "                is limited by the user-specified threshold, the input\n",
    "                array must be masked to contain only valid values.\n",
    "                ``matplotlib`` will handle masked arrays and remove the\n",
    "                out-of-range data from the plot.  Importantly, the\n",
    "                ``transform`` method *must* return an array that is the\n",
    "                same shape as the input array, since these values need to\n",
    "                remain synchronized with values in the other dimension.\n",
    "                \"\"\"\n",
    "                import numpy as np\n",
    "                \n",
    "                return np.exp(self.scale * a)\n",
    "\n",
    "            def inverted(self):\n",
    "                \"\"\"\n",
    "                Override this method so matplotlib knows how to get the\n",
    "                inverse transform for this transform.\n",
    "                \"\"\"\n",
    "                return FlassPlot.ExpScale.InvertedExpTransform(self.scale)\n",
    "\n",
    "        class InvertedExpTransform(mtransforms.Transform):\n",
    "            input_dims = 1\n",
    "            output_dims = 1\n",
    "            is_separable = True\n",
    "\n",
    "            def __init__(self, scale):\n",
    "                from matplotlib import transforms as mtransforms\n",
    "                \n",
    "                mtransforms.Transform.__init__(self)\n",
    "                self.scale = scale\n",
    "\n",
    "            def transform_non_affine(self, a):\n",
    "                import numpy as np\n",
    "                \n",
    "                return np.log(a / self.scale)\n",
    "\n",
    "            def inverted(self):\n",
    "                return FlassPlot.ExpScale.ExpTransform(self.scale)\n",
    "\n",
    "    @staticmethod\n",
    "    def yo():\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.figure(figsize=(4,2))\n",
    "        \n",
    "    @staticmethod\n",
    "    def forpaper():\n",
    "        import matplotlib.pyplot as plt\n",
    "        from matplotlib import scale as mscale\n",
    "\n",
    "        mscale.register_scale(FlassPlot.ExpScale)\n",
    "\n",
    "        SMALL_SIZE = 16\n",
    "        MEDIUM_SIZE = 22\n",
    "        BIGGER_SIZE = 24\n",
    "\n",
    "        plt.rc('font', size=SMALL_SIZE)          # controls default text sizes\n",
    "        plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title\n",
    "        plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "        plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "        plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "        plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "        plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "        \n",
    "    @staticmethod\n",
    "    def exppic(x, y, label, expscale, **kwargs):\n",
    "        import matplotlib.pyplot as plt\n",
    "        import matplotlib.ticker as ticker\n",
    "        plt.ylim(0.0, 1.01)\n",
    "        plt.plot(x, y, label=label, **kwargs)\n",
    "        plt.gca().set_xscale('log')\n",
    "        plt.gca().set_yscale('exp', expscale=expscale)\n",
    "        plt.ylim(0.0, 1.01)\n",
    "        plt.gca().yaxis.set_major_locator(ticker.FixedLocator([0.38,0.68,0.86,0.95,1]))\n",
    "\n",
    "        plt.legend()\n",
    "        \n",
    "    @staticmethod\n",
    "    def pic(x, y, label): \n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.semilogx(x, y, label=label)\n",
    "\n",
    "        #plt.loglog(x, y, label=label)\n",
    "        plt.legend()\n",
    "        \n",
    "    @staticmethod\n",
    "    def axeslabel(xlabel, ylabel):  \n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.xlabel(xlabel)\n",
    "        plt.ylabel(ylabel)\n",
    "        \n",
    "    @staticmethod\n",
    "    def title(title):\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.title(title)\n",
    "        \n",
    "    @staticmethod\n",
    "    def legend(**kwargs):\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.legend(**kwargs)\n",
    "        \n",
    "    @staticmethod\n",
    "    def savefig(filename):\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.savefig(filename, bbox_inches='tight')\n",
    "        \n",
    "    @staticmethod\n",
    "    def plt():\n",
    "        import matplotlib.pyplot as plt\n",
    "        return plt\n",
    "\n",
    "import pickle\n",
    "allres = pickle.load(open( \"epsilongreedy_cidiff_allres.p\", \"rb\" ) )\n",
    "\n",
    "renameit = { \"Asymptotic Gaussian\": \"Gaussian\", \"MLE CI\": \"MLE\", \"Euclidean\": \"EuclidMLE\" }\n",
    "skip = { }\n",
    "FlassPlot.forpaper()\n",
    "for name, res in allres:\n",
    "    if name in skip:\n",
    "        continue\n",
    "    x = [ x[0] for x in res ]\n",
    "    y = [ x[1]['width'] for x in res ]\n",
    "    ylo = [ x[1]['widthlo'] for x in res ]\n",
    "    yhi = [ x[1]['widthhi'] for x in res ]\n",
    "    FlassPlot.plt().semilogx(x, y, label=renameit.get(name, name))\n",
    "    FlassPlot.plt().fill_between(x, ylo, yhi, alpha=0.15)\n",
    "\n",
    "FlassPlot.legend(loc=\"center\", bbox_to_anchor=[0.8,0.825])\n",
    "FlassPlot.axeslabel('n / $w_{max}$', 'CI width')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pickle\n",
    "del allres\n",
    "allres = pickle.load(open( \"epsilongreedy_cidiff_allres.p\", \"rb\" ) )\n",
    "\n",
    "renameit = { \"Asymptotic Gaussian\": \"Gaussian\", \"MLE CI\": \"MLE\", \"Euclidean\": \"EuclidMLE\" }\n",
    "skip = { }\n",
    "FlassPlot.forpaper()\n",
    "for name, res in allres:\n",
    "    if name in skip:\n",
    "        continue\n",
    "    x = [ x[0] for x in res ]\n",
    "    y = [ x[1]['cov'] for x in res ]\n",
    "    ylo = [ x[1]['cov'] - 1.96 * x[1]['covstd'] for x in res ]\n",
    "    yhi = [ x[1]['cov'] + 1.96 * x[1]['covstd'] for x in res ]\n",
    "    FlassPlot.exppic(x, y, label=renameit.get(name, name), expscale=7.0)\n",
    "    FlassPlot.plt().fill_between(x, ylo, yhi, alpha=0.25)\n",
    "FlassPlot.exppic([ x[0] for x in res ], [ 0.95 for x in res ], label='_nolegend_', expscale=7.0, ls='dashed')\n",
    "FlassPlot.legend(loc=\"center\", bbox_to_anchor=[0.8,0.175])\n",
    "FlassPlot.axeslabel('n / $w_{max}$', 'empirical coverage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}