RL CH3.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import clear_output\n",
    "from time import sleep\n",
    "import tensorflow.math as math"
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   "source": [
    "### Exercise 3.12"
   ]
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    "$v_\\pi(s) = \\Sigma_a \\pi(a|s)q_\\pi(s,a)$"
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   "source": [
    "### Exercise 3.13 "
   ]
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   "source": [
    "$q_\\pi(s, a) = \\Sigma_{s',r}p(s',r|s,a)[r+\\gamma v_\\pi(s')]$"
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   "source": [
    "### Exercise 3.17"
   ]
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   "source": [
    "$q_\\pi(s, a) = \\Sigma_{s',r}p(s',r|s,a)[r+\\gamma v_\\pi(s')]$ $\\hspace{1cm}$ (Exercise 3.13)  \n",
    "$v_\\pi(s) = \\Sigma_a \\pi(a|s)q_\\pi(s,a)$ $\\hspace{1cm}$ (Exercise 3.12)  \n",
    "$\\rightarrow q_\\pi(s, a) = \\Sigma_{s',r}p(s',r|s,a)[r+\\gamma \\Sigma_{a'} \\pi(a'|s')q_\\pi(s',a')]$"
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