{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Dynamical System Example "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we have a model of a fixed population of people who are interested in study a Coding Course\n",
    "\n",
    "For Every Intake of the Coding course, 10% will start the course (90% wont!)\n",
    "\n",
    "Of those studying 20% will complete the course, 7% will GIVE up (never to attempt it again!) , 8% will defer their studies, and 65% will remain studying \n",
    "\n",
    "This state transition diagram illustrates the model\n"
   ]
  },
  {
   "attachments": {
    "Codingdiagram.jpg": {
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   },
   "cell_type": "markdown",
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   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
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       "  1070.07,1325.43 1090.77,1329.79 1111.47,1333.84 1132.17,1337.61 1152.87,1341.1 1173.57,1344.34 1194.26,1347.36 1214.96,1350.16 1235.66,1352.75 1256.36,1355.17 \n",
       "  1277.06,1357.41 1297.76,1359.49 1318.45,1361.42 1339.15,1363.22 1359.85,1364.89 1380.55,1366.44 1401.25,1367.87 1421.95,1369.21 1442.64,1370.45 1463.34,1371.6 \n",
       "  1484.04,1372.67 1504.74,1373.67 1525.44,1374.59 1546.14,1375.45 1566.84,1376.24 1587.53,1376.98 1608.23,1377.67 1628.93,1378.3 1649.63,1378.9 1670.33,1379.45 \n",
       "  1691.03,1379.96 1711.72,1380.43 1732.42,1380.87 1753.12,1381.28 1773.82,1381.66 1794.52,1382.01 1815.22,1382.34 1835.92,1382.64 1856.61,1382.93 1877.31,1383.19 \n",
       "  1898.01,1383.43 1918.71,1383.66 1939.41,1383.87 1960.11,1384.07 1980.8,1384.25 2001.5,1384.41 2022.2,1384.57 2042.9,1384.72 2063.6,1384.85 2084.3,1384.98 \n",
       "  2105,1385.09 2125.69,1385.2 2146.39,1385.3 2167.09,1385.39 2187.79,1385.48 2208.49,1385.56 2229.19,1385.64 2249.88,1385.71 2270.58,1385.77 2291.28,1385.83 \n",
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       "  656.104,1290.28 676.802,1297.14 697.501,1303.51 718.199,1309.43 738.898,1314.93 759.596,1320.04 780.294,1324.79 800.993,1329.19 821.691,1333.29 842.39,1337.09 \n",
       "  863.088,1340.62 883.787,1343.9 904.485,1346.94 925.184,1349.77 945.882,1352.4 966.581,1354.84 987.279,1357.1 1007.98,1359.2 1028.68,1361.16 1049.37,1362.97 \n",
       "  1070.07,1364.66 1090.77,1366.22 1111.47,1367.68 1132.17,1369.03 1152.87,1370.28 1173.57,1371.44 1194.26,1372.52 1214.96,1373.53 1235.66,1374.46 1256.36,1375.33 \n",
       "  1277.06,1376.13 1297.76,1376.88 1318.45,1377.57 1339.15,1378.22 1359.85,1378.81 1380.55,1379.37 1401.25,1379.89 1421.95,1380.37 1442.64,1380.81 1463.34,1381.22 \n",
       "  1484.04,1381.61 1504.74,1381.96 1525.44,1382.3 1546.14,1382.6 1566.84,1382.89 1587.53,1383.15 1608.23,1383.4 1628.93,1383.63 1649.63,1383.84 1670.33,1384.04 \n",
       "  1691.03,1384.22 1711.72,1384.39 1732.42,1384.55 1753.12,1384.7 1773.82,1384.83 1794.52,1384.96 1815.22,1385.08 1835.92,1385.19 1856.61,1385.29 1877.31,1385.38 \n",
       "  1898.01,1385.47 1918.71,1385.55 1939.41,1385.63 1960.11,1385.7 1980.8,1385.76 2001.5,1385.82 2022.2,1385.88 2042.9,1385.93 2063.6,1385.98 2084.3,1386.02 \n",
       "  2105,1386.06 2125.69,1386.1 2146.39,1386.14 2167.09,1386.17 2187.79,1386.2 2208.49,1386.23 2229.19,1386.26 2249.88,1386.28 2270.58,1386.31 2291.28,1386.33 \n",
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       "  449.119,987.821 469.818,948.167 490.516,911.118 511.215,876.572 531.913,844.402 552.612,814.473 573.31,786.645 594.008,760.78 614.707,736.746 635.405,714.417 \n",
       "  656.104,693.676 676.802,674.41 697.501,656.516 718.199,639.897 738.898,624.462 759.596,610.126 780.294,596.813 800.993,584.448 821.691,572.965 842.39,562.301 \n",
       "  863.088,552.397 883.787,543.199 904.485,534.656 925.184,526.723 945.882,519.355 966.581,512.513 987.279,506.158 1007.98,500.257 1028.68,494.776 1049.37,489.686 \n",
       "  1070.07,484.959 1090.77,480.569 1111.47,476.492 1132.17,472.705 1152.87,469.189 1173.57,465.923 1194.26,462.89 1214.96,460.074 1235.66,457.458 1256.36,455.028 \n",
       "  1277.06,452.772 1297.76,450.677 1318.45,448.731 1339.15,446.924 1359.85,445.246 1380.55,443.687 1401.25,442.239 1421.95,440.895 1442.64,439.646 1463.34,438.487 \n",
       "  1484.04,437.41 1504.74,436.41 1525.44,435.481 1546.14,434.619 1566.84,433.818 1587.53,433.074 1608.23,432.383 1628.93,431.741 1649.63,431.145 1670.33,430.592 \n",
       "  1691.03,430.078 1711.72,429.601 1732.42,429.157 1753.12,428.746 1773.82,428.363 1794.52,428.008 1815.22,427.679 1835.92,427.372 1856.61,427.088 1877.31,426.824 \n",
       "  1898.01,426.579 1918.71,426.351 1939.41,426.139 1960.11,425.943 1980.8,425.76 2001.5,425.591 2022.2,425.433 2042.9,425.287 2063.6,425.152 2084.3,425.025 \n",
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       "  449.119,1247.03 469.818,1233.15 490.516,1220.19 511.215,1208.1 531.913,1196.84 552.612,1186.36 573.31,1176.62 594.008,1167.57 614.707,1159.16 635.405,1151.34 \n",
       "  656.104,1144.08 676.802,1137.34 697.501,1131.08 718.199,1125.26 738.898,1119.86 759.596,1114.84 780.294,1110.18 800.993,1105.85 821.691,1101.83 842.39,1098.1 \n",
       "  863.088,1094.63 883.787,1091.41 904.485,1088.42 925.184,1085.65 945.882,1083.07 966.581,1080.67 987.279,1078.45 1007.98,1076.39 1028.68,1074.47 1049.37,1072.69 \n",
       "  1070.07,1071.03 1090.77,1069.49 1111.47,1068.07 1132.17,1066.74 1152.87,1065.51 1173.57,1064.37 1194.26,1063.31 1214.96,1062.32 1235.66,1061.41 1256.36,1060.56 \n",
       "  1277.06,1059.77 1297.76,1059.03 1318.45,1058.35 1339.15,1057.72 1359.85,1057.13 1380.55,1056.59 1401.25,1056.08 1421.95,1055.61 1442.64,1055.17 1463.34,1054.77 \n",
       "  1484.04,1054.39 1504.74,1054.04 1525.44,1053.71 1546.14,1053.41 1566.84,1053.13 1587.53,1052.87 1608.23,1052.63 1628.93,1052.4 1649.63,1052.2 1670.33,1052 \n",
       "  1691.03,1051.82 1711.72,1051.66 1732.42,1051.5 1753.12,1051.36 1773.82,1051.22 1794.52,1051.1 1815.22,1050.98 1835.92,1050.88 1856.61,1050.78 1877.31,1050.68 \n",
       "  1898.01,1050.6 1918.71,1050.52 1939.41,1050.44 1960.11,1050.38 1980.8,1050.31 2001.5,1050.25 2022.2,1050.2 2042.9,1050.15 2063.6,1050.1 2084.3,1050.05 \n",
       "  2105,1050.01 2125.69,1049.98 2146.39,1049.94 2167.09,1049.91 2187.79,1049.88 2208.49,1049.85 2229.19,1049.82 2249.88,1049.8 2270.58,1049.77 2291.28,1049.75 \n",
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       "1626.13,433.164 2280.76,433.164 2280.76,130.764 1626.13,130.764 \n",
       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip0700)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1626.13,433.164 2280.76,433.164 2280.76,130.764 1626.13,130.764 1626.13,433.164 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip0700)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1650.13,191.244 1794.13,191.244 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip0700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1818.13, 208.744)\" x=\"1818.13\" y=\"208.744\">Potential Students</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip0700)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1650.13,251.724 1794.13,251.724 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip0700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1818.13, 269.224)\" x=\"1818.13\" y=\"269.224\">Studying</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip0700)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1650.13,312.204 1794.13,312.204 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip0700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1818.13, 329.704)\" x=\"1818.13\" y=\"329.704\">Completed Course </text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip0700)\" style=\"stroke:#c271d2; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  1650.13,372.684 1794.13,372.684 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip0700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1818.13, 390.184)\" x=\"1818.13\" y=\"390.184\">Dropped Forever</text>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 100;\n",
    "A = [ 0.9 0.08 0 0 ; \n",
    "      0.1 0.65 0 0 ;\n",
    "      0   0.20 1 0 ; \n",
    "      0   0.07 0 1 ];\n",
    "x_1 = [1,0,0,0];\n",
    "state_traj = [x_1 zeros(4,T-1) ]; # State trajectory\n",
    "for t=1:T-1 # Dynamics recursion\n",
    "  state_traj[:,t+1] = A*state_traj[:,t];\n",
    "end\n",
    "println(7/(7+20)) #, remove this troy before submisison\n",
    "println(20/(7+20))\n",
    "using Plots\n",
    "plot(1:T, state_traj', xlabel = \"Time t\",\n",
    "label = [\"Potential Students\", \"Studying\", \"Completed Course \", \"Dropped Forever\"])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-Learning Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now going to demonstrate Q-Learning using a  model from the same environment.\n",
    "\n",
    "Imagine the government wants to encourage people to study by offering scholarships ...\n",
    "Lets start by representing represent people's interest in this course by a Level, L  1- 10 , and assume that in any period this is equaly likely to increase(50%)  or decrease. Our model then says  that offering the scholarships causes the interest in the course to increase 75% of the time, but there is a varying cost 0-2.0 , associated with providing the scholarships.  \n",
    "\n",
    "The aim is to use Q learning to determine the optimum choice of offering scholarships or not, dependent upon the cost of offering them and the current interest level L. \n",
    "\n",
    "The Q Learning algorithm uses the following formula to progressively estimate the \"Quality\" of a state and the action to take in that state\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$newQ_{S,A}=(1-\\alpha)Q_{S,A}+\\alpha(R_{S,A}, +\\gamma max(Q'_{S',A'}))$$\n",
    "\n",
    "Where $\\alpha$ is the learning rate. $\\alpha=0$: old knowledge is the only important, $\\alpha=1$: new knowledge is the only important.\n",
    "\n",
    "$\\gamma$ is the discount factor. $\\gamma=0$: short-term reward is only considered, $\\gamma =1$: long-term reward is only considered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.694549 seconds (4.93 M allocations: 140.502 MiB, 7.52% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24.000000000000007, 0.5, 'Enthusiasm L')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra, StatsBase, PyPlot, Random\n",
    "\n",
    "L = 10\n",
    "p0, p1 = 0.50, 0.75\n",
    "beta = 0.75\n",
    "pExplore(t) = t^-0.2\n",
    "alpha(t) = t^-0.2\n",
    "T = 10^6\n",
    "Random.seed!(4)\n",
    "\n",
    "function QlearnSim(Cost)\n",
    "    P0 = diagm(1=>fill(p0,L-1)) + diagm(-1=>fill(1-p0,L-1))\n",
    "    P0[1,1], P0[L,L] = 1 - p0, p0\n",
    "\n",
    "    P1 = diagm(1=>fill(p1,L-1)) + diagm(-1=>fill(1-p1,L-1))\n",
    "    P1[1,1], P1[L,L] = 1 - p1, p1\n",
    "\n",
    "    R0 = collect(1:L)\n",
    "    R1 = R0 .- Cost\n",
    "\n",
    "    nextState(s,a) = a == 0 ? sample(1:L,weights(P0[s,:])) : sample(1:L,weights(P1[s,:]))\n",
    "\n",
    "    Q = zeros(L,2)\n",
    "    s = 1\n",
    "    optimalAction(s) = Q[s,1] >= Q[s,2] ? 0 : 1\n",
    "    for t in 1:T\n",
    "        if rand() < pExplore(t)\n",
    "            a = rand([0,1])\n",
    "        else\n",
    "            a = optimalAction(s)\n",
    "        end\n",
    "        sNew = nextState(s,a)\n",
    "        r = a == 0 ? R0[sNew] : R1[sNew]\n",
    "        Q[s,a+1]=(1-alpha(t))*Q[s,a+1]+alpha(t)*(r+beta*max(Q[sNew,1],Q[sNew,2]))\n",
    "        s = sNew\n",
    "    end\n",
    "    [optimalAction(s) for s in 1:L]\n",
    "end\n",
    "\n",
    "T = 10^6\n",
    "Random.seed!(4)\n",
    "\n",
    "function  learn_and_graph() \n",
    "    CostGrid = 0.0:0.1:2.0\n",
    "    policyMap = zeros(L,length(CostGrid))\n",
    "\n",
    "    for (i,Cost) in enumerate(CostGrid)\n",
    "        policyMap[:,i] = QlearnSim(Cost)\n",
    "    end\n",
    "\n",
    "    imshow(policyMap, cmap=\"bwr\")\n",
    "    xticks(0:2:20, 0:0.2:2); yticks(0:L-1, 1:L)\n",
    "    xlabel(\"Cost\"); ylabel(\"Enthusiasm L\")\n",
    "end\n",
    "\n",
    "T = 10^4\n",
    "Random.seed!(1)\n",
    "@time learn_and_graph() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  3.887529 seconds (43.26 M allocations: 1.040 GiB, 7.12% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24.000000000000007, 0.5, 'Enthusiasm L')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 10^5\n",
    "Random.seed!(1)\n",
    "@time learn_and_graph() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  3.186430 seconds (43.26 M allocations: 1.040 GiB, 6.87% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24.000000000000007, 0.5, 'Enthusiasm L')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 10^5\n",
    "Random.seed!(2)\n",
    "@time learn_and_graph() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "343.573013 seconds (4.32 G allocations: 102.642 GiB, 6.70% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24.000000000000007, 0.5, 'Enthusiasm L')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 10^7\n",
    "Random.seed!(1)\n",
    "@time learn_and_graph() "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.1.1",
   "language": "julia",
   "name": "julia-1.1"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}