reinforcement_learning_exercise_solution.ipynb

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    "# 《Reinforcement Learning, Second Edition 2018》练习的解答\n",
    "\n",
    "这部分是我对2018年第二版的书本上的练习的个人尝试解答。"
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    "### Chapter 3\n",
    "\n",
    "### Exercise 3.12\n",
    "\n",
    "在这里选择的策略是四个方向上等概率移动，因此：$\\pi(a|s) = \\frac{1}{4}$，且给定s和a，s'和r也是固定的。在这个问题中，r都是0，$p(s',r|s,a)=1$。\n",
    "\n",
    "代入Bellman Equation：\n",
    "$$v_{\\pi}(s) = \\sum_a\\pi(a|s)\\sum_{s',r}p(s',r|s,a)[r+\\gamma v_{\\pi}(s')] \\\\=\\frac{1}{4}*1*(0+0.9*0.4) + \\frac{1}{4}*1*(0+0.9*-0.4) + \\frac{1}{4}*1*(0+0.9*0.7) + \\frac{1}{4}*1*(0+0.9*2.3)=0.675$$\n",
    "保留一位小数为0.7，和图中一样。"
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    "### Exercise 3.15\n",
    "\n",
    "$$q_{\\pi}(s,a) = \\sum_{s'}p(s',r|s,a)[r+\\gamma \\sum_{a'}q(s',a')]$$    "
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