CartPole Pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cosmetic-gabriel",
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ethical-satisfaction",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exciting-fellowship",
   "metadata": {},
   "source": [
    "The four values are position, velocity, angle, angular velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "norman-behavior",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.02826596, -0.04967754, -0.00991669, -0.01205246], dtype=float32)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dependent-radius",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "forward-tribute",
   "metadata": {},
   "outputs": [],
   "source": [
    "action = 1 # accelerate right\n",
    "obs, reward, done, info = env.step(action)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "developing-lightning",
   "metadata": {},
   "source": [
    "# Policy Gradiant"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "characteristic-laser",
   "metadata": {},
   "source": [
    "We first make a basic policy which is to hit left if the rod is leaning left and vice versa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "disturbed-aging",
   "metadata": {},
   "outputs": [],
   "source": [
    "def basic_policy(obs): \n",
    "    angle = obs[2]\n",
    "    return 0 if angle<0 else 1\n",
    "\n",
    "totals = []\n",
    "for episode in range(500):\n",
    "    episode_rewards = 0 \n",
    "    obs = env.reset()\n",
    "    for step in range(200):\n",
    "        action = basic_policy(obs)\n",
    "        obs, reward, done, info = env.step(action) \n",
    "        episode_rewards += reward\n",
    "        if done:\n",
    "            break\n",
    "    totals.append(episode_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "recovered-confusion",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42.162, 9.340650726796287, 24.0, 68.0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.mean(totals), np.std(totals), np.min(totals), np.max(totals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bacterial-longer",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_obs=[]\n",
    "\n",
    "obs = env.reset()\n",
    "all_obs.append(obs)\n",
    "\n",
    "for step in range(200):\n",
    "    action = basic_policy(obs)\n",
    "    obs, reward, done, info = env.step(action)\n",
    "    all_obs.append(obs)\n",
    "    episode_rewards += reward\n",
    "    if done:\n",
    "        break\n",
    "all_obs=np.stack(all_obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "prostate-divorce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fccd83f6160>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "mpl.rcParams['figure.figsize'] = [15.0, 5.0]\n",
    "plt.plot(all_obs[:,0],label='position')\n",
    "plt.plot(all_obs[:,2],label='angle')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cubic-parish",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "import torch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "humanitarian-abortion",
   "metadata": {},
   "source": [
    "Now we make a DNN policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "adjusted-alfred",
   "metadata": {},
   "outputs": [],
   "source": [
    "class RLPolicy(nn.Module):\n",
    "    \n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.model=nn.Sequential(nn.Linear(4,5),\n",
    "                      nn.ELU(),\n",
    "                      nn.Linear(5,1),\n",
    "                      nn.Sigmoid()\n",
    "                     )\n",
    "        \n",
    "    def forward(self,x):\n",
    "        if isinstance(x,np.ndarray):\n",
    "            x=torch.tensor(x)\n",
    "        return self.model(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "surprising-bench",
   "metadata": {},
   "source": [
    "This plays one step and returns the probability of going left. The action itself is chose to be 0 or 1 with that probability. The target has to be chosen carefully. The output of the model is for going left but we don't always go left. If we go right then from the models point of view we went opposite to it's recommendation so the target should be 0 and if we go left then from the models point of view we went along with it's recommendation so the target should be 1.\n",
    "\n",
    "The loss is computed with this and the grads are computed and returned along with the env variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "careful-performer",
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_one_step(env, obs, model, loss_fn):\n",
    "    left_proba = model(obs[np.newaxis])\n",
    "    action = torch.rand([1,1])>left_proba\n",
    "    y_target = torch.tensor([[1.]]) - action.type(torch.float32)\n",
    "    loss =loss_fn(left_proba,y_target)\n",
    "    loss.backward()\n",
    "    grads=[torch.clone(x.grad) for x in model.parameters()]\n",
    "    [x.grad.data.zero_() for x in model.parameters()]\n",
    "    obs, reward, done, info = env.step(int(action[0, 0].numpy())) \n",
    "    return obs, reward, done, grads\n",
    "#play_one_step(env,obs,model,loss_fn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "simple-bloom",
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_multiple_episodes(env, n_episodes, n_max_steps, model, loss_fn): \n",
    "    all_rewards = []\n",
    "    all_grads = []\n",
    "    for episode in range(n_episodes):\n",
    "        current_rewards = [] \n",
    "        current_grads = []\n",
    "        obs = env.reset()\n",
    "        for step in range(n_max_steps):\n",
    "            obs, reward, done, grads = play_one_step(env, obs, model, loss_fn) \n",
    "            current_rewards.append(reward)\n",
    "            current_grads.append(grads)\n",
    "            if done:\n",
    "                break\n",
    "        all_rewards.append(current_rewards)\n",
    "        all_grads.append(current_grads) \n",
    "    return all_rewards, all_grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "boring-security",
   "metadata": {},
   "outputs": [],
   "source": [
    "def discount_rewards(rewards, discount_factor): \n",
    "    discounted = np.array(rewards)\n",
    "    for step in range(len(rewards) - 2, -1, -1):\n",
    "        discounted[step] += discounted[step + 1] * discount_factor \n",
    "    return discounted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "laden-therapy",
   "metadata": {},
   "outputs": [],
   "source": [
    "def discount_and_normalize_rewards(all_rewards, discount_factor): \n",
    "    all_discounted_rewards = [discount_rewards(rewards, discount_factor)\n",
    "                              for rewards in all_rewards] \n",
    "    flat_rewards = np.concatenate(all_discounted_rewards)\n",
    "    reward_mean = flat_rewards.mean()\n",
    "    reward_std = flat_rewards.std()\n",
    "    return [(discounted_rewards - reward_mean) / reward_std\n",
    "            for discounted_rewards in all_discounted_rewards]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "resistant-dallas",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-22, -40, -50])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_rewards([10, 0, -50], discount_factor=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "proper-federation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([-0.28435071, -0.86597718, -1.18910299]),\n",
       " array([1.26665318, 1.0727777 ])]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_and_normalize_rewards([[10, 0, -50], [10, 20]], discount_factor=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "answering-overhead",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iterations = 150\n",
    "n_episodes_per_update = 10\n",
    "n_max_steps = 200\n",
    "discount_factor = 0.95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "designing-writer",
   "metadata": {},
   "outputs": [],
   "source": [
    "model=RLPolicy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "subject-summer",
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.Adam(model.parameters(),lr=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "green-narrative",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_fn=torch.nn.BCELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "independent-shaft",
   "metadata": {},
   "outputs": [],
   "source": [
    "for iteration in range(n_iterations):\n",
    "    all_rewards, all_grads = play_multiple_episodes(env, \n",
    "                                                    n_episodes_per_update, \n",
    "                                                    n_max_steps,\n",
    "                                                    model, \n",
    "                                                    loss_fn\n",
    "                                                   )\n",
    "    all_final_rewards = discount_and_normalize_rewards(all_rewards,\n",
    "                                                       discount_factor\n",
    "                                                      )\n",
    "    for var_index,var in enumerate(model.parameters()):\n",
    "        grads=[]\n",
    "        for episode_index, final_rewards in enumerate(all_final_rewards):\n",
    "            for step, final_reward in enumerate(final_rewards):\n",
    "                grads.append(final_reward * all_grads[episode_index][step][var_index])\n",
    "        mean_grads=torch.stack(grads,0).mean(0)\n",
    "        var.grad.data=mean_grads\n",
    "    optimizer.step()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "promising-officer",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_obs=[]\n",
    "obs = env.reset()\n",
    "all_obs.append(obs)\n",
    "for step in range(200):\n",
    "    left_prob = model(obs)\n",
    "    action = int(left_prob.detach().numpy()[0]<.5)\n",
    "    obs, reward, done, info = env.step(action) \n",
    "    all_obs.append(obs)\n",
    "    episode_rewards += reward\n",
    "    if done:\n",
    "        break\n",
    "all_obs=np.stack(all_obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "norman-channels",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcd187a3ca0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(all_obs[:,0],label='position')\n",
    "plt.plot(all_obs[:,2],label='angle')\n",
    "plt.plot\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "anticipated-blood",
   "metadata": {},
   "outputs": [],
   "source": [
    "totals = []\n",
    "for episode in range(500):\n",
    "    episode_rewards = 0 \n",
    "    obs = env.reset()\n",
    "    for step in range(200):\n",
    "        left_prob = model(obs)\n",
    "        obs, reward, done, info = env.step(int(left_prob.detach().numpy()[0]<.5)) \n",
    "        episode_rewards += reward\n",
    "        if done:\n",
    "            break\n",
    "    totals.append(episode_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "future-columbia",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200.0, 0.0, 200.0, 200.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(totals), np.std(totals), np.min(totals), np.max(totals)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seven-rebel",
   "metadata": {},
   "source": [
    "# Markov Decision Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "chief-signature",
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_probabilities = [ # shape=[s, a, s']\n",
    "[[0.7, 0.3, 0.0], [1.0, 0.0, 0.0], [0.8, 0.2, 0.0]], [[0.0, 1.0, 0.0], None, [0.0, 0.0, 1.0]],\n",
    "[None, [0.8, 0.1, 0.1], None]]\n",
    "\n",
    "rewards = [ # shape=[s, a, s']\n",
    "[[+10, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0], [0, 0, -50]], [[0, 0, 0], [+40, 0, 0], [0, 0, 0]]]\n",
    "\n",
    "possible_actions = [ [i for i,a in enumerate(s) if a] for s in transition_probabilities ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "responsible-crack",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1, 2], [0, 2], [1]]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "possible_actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "coordinated-layout",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_values = np.full((3, 3), -np.inf) # -np.inf for impossible actions \n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0 # for all possible actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "golden-oregon",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   0.],\n",
       "       [  0., -inf,   0.],\n",
       "       [-inf,   0., -inf]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "seeing-humanitarian",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_vals_1=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "rolled-marriage",
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.95 # the discount factor\n",
    "for iteration in range(50): \n",
    "    Q_prev = Q_values.copy() \n",
    "    for s in range(3):\n",
    "        for a in possible_actions[s]: \n",
    "            Q_values[s, a] = np.sum([transition_probabilities[s][a][sp] \n",
    "                                     * (rewards[s][a][sp] + gamma * np.max(Q_prev[sp])) for sp in range(3)\n",
    "                                    ]\n",
    "                                   )\n",
    "    Q_vals_1.append(Q_values[0].copy())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "psychological-nelson",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[21.73304188, 20.63807938, 16.70138772],\n",
       "       [ 0.95462106,        -inf,  1.01361207],\n",
       "       [       -inf, 53.70728682,        -inf]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "superior-decision",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 1])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values.argmax(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "controlling-recruitment",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_vals_1=np.array(Q_vals_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "annoying-festival",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fccc85ab760>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+4347QP9E/y/2A+3L2J6cz+m/fdr9/n52gH3+ugc6foCQM5z9GsoYGfoqQ5jKFK6CsOga6YN3BjP3MBHOiozjWH3hFy8qGg7pm39+towxQZcEAED56feFPiE58dSX+L71AdqduLfPSeszUFui/3rf0kkbL32MDH1ParcZ2jKM4Q8vJ7Ul+zv958vYnjwuLcwk95UyE5ZMKPUJJbdN//a+j3+/Ofn4vs9Ax/vniZ7muFOMISOFvOVp5zZp/TIcI3PqufuOT++Xvi/TeGntoycH97/3MBHOisxPnt2pZ1sO6zsfPFuTxlQFXQ4AoNwkryQ4MS9A+AKHE5cSsf7b6fv7jjtVH/92YhB9kuEk03H+kJRsTxsnY3BKDLydbCt0yS/4obBvGUrbTrYNpq/XJ1JxclsonAoQ/cb1BYqT+of6z9Fv3QxinFDm/QP1SR8zY0AaaJ5kn3CG9kxhKEOIAQaBcFZE3jzUqW/9rlmXzR2vD711atDlAABOxXHcIJKIpZZ96/G0ff7teGqZaV/fft++fsf4A9JA++ID93Xi3rj+MJVI9S2EUBKKSqGI+yW43zKS+vKc3A6FM++PVKa1h/qP1TfOqbYjbqhJnzf5BX1Q7WlBacA23/EZQ1QkQ5AiEADFhnBWJBzH6gu/fEEhY/TNP38LtzMCKB9Owgs2vb7lKdaduK/dW+8LR8m+yXDj2+7XLy1Q9Y07yHUn5j1nkQ/G/WIejnqhJZxhPZJhX0SKVvtCTMTXN5Kh3R940rZPtz89QIUiUtgXlsLpYStTyEp+eNE0gNJFOCsS965/U8+8cVjf+vO3aPLY6qDLAVBKnIQU75ESPVK817f01hMxb7/XFvfaEl5bxr7+4OT/xNKOSQ9Z6W05vlITikrhCjccJENLcj1ckQoeyfVodYb2qBc0kmNFUuP4Q1P6HP32+Y+JpoJLpr7+gJUMRQCAkkA4KwKthzv1zd9u0yVzGvXht00LuhwAI2WtF2K6vaDS7QaaeE9aW69vOxmeelJBKXlccv9JAcu376Slr1+2r/CEK6RwZSq8JMNPJK2tokYKj/X18YWkTMcPuO4LWCFvnlDE1yfiC1H+vhFu+wIAFBTCWYGz1urWB19UyBh96xrezghkjZOQYl1eqPGW/ba7pVi3LzgNZek/zh+6fNvZeK2wCUmRKjdsRCq98JNcJtuq3N95SW6HK92H+ZPhJ72tb1/FAOvR1PjJT7/tKIEHAIBhIpwVuJ+tb9WTrx3S//jAWzSF2xlRqqz1wlBX6hP3r3cPvOwLUV1py+5Thy8nPrKaw17wiQywrBqb1uYLTpEqN+xEqgZoq8hwXIWvr9cW5v/CAQAoJfxlL2C7jnTqG795WUtnN+qjS7idEQHou7rULcU6vbCUvvR/Mu3rTAtb3lh9Y3qBargiVe4nWt1/GamSqkZLkWopWpVqi1SdvB2p9I6rdPv7t8OVXv/qVIgKV/BSAgAAkHWEswJlrdWXHnxJVuLtjMgsebWpt1OKnXCXvSdS6+ltJwWo9PDUffK+RM8wCjNStMYNN8lPpEqqqJUq6qTaCW7YiVZ7wcnfL9N2Vf/1fuGpilvoAABAySCcFaj7nmvV2lcP6mvvX6Rp9TVBl4NcSMSkrqNS99HUsrtd6jrSv63La+8+KvUcdwNUMnwN5UUOJpQWmmq8q0g17jNJ0UmZ90XTAlNfW01a3+R6JYEJAABgGAhnBWj30S59/TfbdNGsBl23ZHrQ5WAoejul4/ukDu9zfL/UsVfq2O+2Hz+QClyxE6ceKxmaqsZK1WOl0VOlyjr3ClS01n3TXbTGuyJVm1ofqI3QBAAAUNAIZwUmeTujY62+88GzFQrxZbogWCudOCgdek06ttsLXvvc0NWx1wth+6We9pOPDUWlUZPcz7gmqXqcG7qqx6aC10nLMW6YAgAAQNkgnBWYBzbs0ppXDuirVy/kdsYg9HRIh153Q1jf0ltPD16RKqluohu6JpwlzVoujZoojToj1T7qDDeMccUKAAAAp0E4KyB727v0td+8rAtm1uvjF8wIupzSFe+Vju50Q9fBV/sHseP7fB2NNGaa1HCmdPa1UsNsd33MNDeEVY0ldAEAACBrThvOjDF3SnqvpDZr7SKv7SuSPi3pgNftNmvtb3NVZDmw1uq2B19SLOFwO2M2WSsdfkPa9ZzU+qzU+pzU9rJkE6k+NQ1u8Jp9uRu+Gua42/Uz3ZdcAAAAAHkwmCtnP5b0fyTdndb+PWvt/8x6RWXql5t2a9X2A/ry+xZoRkNt0OUUr95Oac9mN4jtek5qXS91HnT3VYySpi6Wlt4sNc71AtgsqaY+0JIBAAAAaRDhzFq7xhjTlIdayta+9m7966NbtaSpXjdc1BR0OcXDWqm91Q1greulXeulfS9JTtzd3zBbmvNOadoS9zN+vhQKB1szAAAAMICRPHP2WWPM9ZI2SLrFWnskSzWVFWutbnvIvZ3x29zOeHpHW6XmX0s7n3IDWfIZsWiNNOWt0sWfk6Yukaa+TaptCLZWAAAAYAiGG87+r6SvSbLe8n9J+lSmjsaYmyTdJEnTp/ObXeke2rxbK5vb9M/vXaCZjdzOmFH7Lunlh6WtD7m3KkruK+lnXpq6KjZhoRTm/TYAAAAoXsP6Nmut3Z9cN8b8h6Rfn6Lv7ZJul6TFixfb4cxXqtqOdesrj2zVW2eM0yff3hR0OYXl2N5UIGt9xm2bdLZ0+Zelhe93nxUDAAAASsiwwpkx5gxr7V5v8wOStmSvpPLxjd9uU0/cfTtjmNsZ3R9x3vaItOVB6c2nJVlp4iJpxT9JCz4gNc4OukIAAAAgZwbzKv2fSVomqdEYs0vSlyUtM8acK/e2xh2S/ip3JZamXUc69egLe/SXl8zSmePrgi4nOMcPSNselrb+StqxTpKVxp8lLfuStPAD0vi5QVcIAAAA5MVg3tb40QzNd+SglrJy11M7ZIwpz9sZu466tytufUjasVayjvvbYpd9wQ1kE84KukIAAAAg73iDQgCO98T18/WtumrRJE0eW0Y/ctzdLj3zI+npH0o97VL9mdIlt3iBbIFkuLUTAAAA5YtwFoAHNrSqoyeuG5fODLqU/OjpkJ79f9JTP5C6j0rz3iNdeos0+XwCGQAAAOAhnOVZwrH6ryd36PzpY3Xe9HFBl5NbPcel5/5DevJ/S12HpblXSstulSafF3RlAAAAQMEhnOXZH7ft15uHO/XFK+cHXUru9HZKz/2n9OT3pc5D0uwr3Bd8TH1r0JUBAAAABYtwlmd3rGvRlLHVetfCiUGXkn2xLmnDndK670sn2qQzV7ihbNqSoCsDAAAACh7hLI+27G7X+pbD+sd3n6VIOBR0OdkT65Y2/lha9z3p+D5p5qXSsrulGRcFXRkAAABQNAhneXTnuhbVVoT14SXTgi4lO+I90qa7pbXflTr2SDMulj54h9S0NOjKAAAAgKJDOMuTtmPdevTFPbrughkaXRUNupyRcRxp8z3S6u9Ix3ZJ0y6UPvAj94oZb18EAAAAhoVwlid3P71TccfqLy5uCrqUkek8LP3qM9Irj0lT3yZd/QNp1nJCGQAAADBChLM86I4ldO+zO3XFWRM1o6E26HKGb/dG6f5PSh17pav+TVryaUIZAAAAkCWEszx4cNNuHemM6VPF+qPT1krr/0P6/W3SqDOkT/2e1+IDAAAAWUY4yzFrre58skULJ4/WBTPrgy5n6Ho6pEf+Rtr6kDTnXe6zZTVF+M8BAAAAFDjCWY6tfuWAXms7ru9ee45Msd0CuH+rdP/10uE3pMu/LF18sxQqoZ8AAAAAAAoI4SzH7ljXogmjKvXesycHXcrQbL5X+s0tUtVo6YZHeT0+AAAAkGOEsxx6ZX+H1r56UJ9/51xVRIrkilOsS/rt56XNP5GaLpGuuUMaNTHoqgAAAICSRzjLoTvXtagyEtLHLpgRdCmDc+h19zbG/VukSz4vLb9NCoWDrgoAAAAoC4SzHDl0vEcPbt6ta86fqvraiqDLOb2tv5Ie/qwUjkjX/UKac0XQFQEAAABlhXCWI/c++6Z6445uXNoUdCmnFu+VHv9n6dkfSVMWSx/6sTR2WtBVAQAAAGWHcJYDPfGE7n56py6bO16zJ4wKupyBHW2VHviktHuDdMFnpCu+KkWK4CofAAAAUIIIZznw6At7dfB4j24s5B+dfmO19MANUiIufeguaeH7g64IAAAAKGuEsyyz1uqOdS2aO7FOl8xpDLqczPY8L/3so9LY6dJH7pUazgy6IgAAAKDsFcn73YvH028c0ra9x/Spi2cW5o9OH31T+um1Uk29dP2vCGYAAABAgeDKWZbdua5F9bUVev95U4Iu5WRdR6V7PyTFuqXrH5ZGTQq6IgAAAAAerpxlUcvBE3qiuU0fv2C6qqIF9vtg8V7pvo+7v2X2kZ9IE84KuiIAAAAAPlw5y6IfP9miaCikj19UYD86ba30yGelHWulD9wuzbw06IoAAAAApOHKWZa0d8X0wMZdet85kzVhVFXQ5fS36hvSi/dJK/5JOufDQVcDAAAAIAPCWZb8fP2b6uxNFN7r8zfdLa35N+n866VLPh90NQAAAAAGQDjLgnjC0V1P7dBFsxq0YPLooMtJee2P0qM3S2deLr3nu1Ihvj0SAAAAgCTCWVb8bss+7WnvLqyrZntflO6/QZqwQLr2LikcDboiAAAAAKdAOMuCO9a1aGZjrVbMnxB0Ka72Xe5vmVWNka67X6ocFXRFAAAAAE6DcDZCG3ce0fOtR/UXFzcpFCqA2wa7293fMus9IV33gDR6ctAVAQAAABgEXqU/Qneua9HoqoiuOX9q0KW4v2V2//XSwVek634hTVwYdEUAAAAABokrZyOw52iXfrdlrz66ZLpqKwPOudZKj35OeuNP0p/9QDpzebD1AAAAABgSwtkI/GHrPjlW+siS6UGXIq3+tvTCT6VlX5LO/VjQ1QAAAAAYIsLZCKzcfkCzGms1s7E22EI23yv96ZvSuddJl30x2FoAAAAADAvhbJhO9MT1zOuHtDzoNzS+vkp69G+lWcuk936f3zIDAAAAihThbJiefO2gehNOsK/P37dFuu8TUuM86dq7pUhFcLUAAAAAGBHC2TCt2t6musqI3tZUH0wBnYfd3zKrrHN/y6xqTDB1AAAAAMgKXqU/DNZarWo+oEvmNKoiElC+Xfl1qWOf9OknpDEF8Bp/AAAAACPClbNheHnvMe071h3c82b7tkgb/0t6243S5POCqQEAAABAVhHOhmFVc5skadm88fmf3FrpsVulqrHua/MBAAAAlATC2TCsbG7T2VPHaMKoqvxPvu0RacdaacU/SjUBPe8GAAAAIOsIZ0N0+ESvNrce1fJ5AdzSGOuSfv9P0oSF0vmfzP/8AAAAAHKGF4IM0epX2mStgnmF/lM/kNrflG74tRTmfzoAAACglHDlbIhWNh9QY12l3jIlz6+ub98lrf2utOBqaeYl+Z0bAAAAQM4RzoYgnnC0enubls0br1DI5Hfyx78syUpXfC2/8wIAAADIC8LZEGzceUTHuuO6PN+3NO58WtryC+ntfyuNm5HfuQEAAADkBeFsCFZub1M0bLR0TmP+JnUS0u++II2eIi29OX/zAgAAAMir04YzY8ydxpg2Y8wWX1u9MeZxY8yr3nJcbsssDKua2/S2pnqNqormb9LNP5H2vShd8VWpojZ/8wIAAADIq8FcOfuxpCvT2m6V9IS1do6kJ7ztkrbrSKde2X88v29p7G6XnviqNO1CadE1+ZsXAAAAQN6dNpxZa9dIOpzWfLWku7z1uyS9P7tlFZ5VzW2SpOX5DGervyN1HpKu+rZk8vwCEgAAAAB5NdxnziZaa/d66/skTcxSPQVrZXObZjTUaFZjnm4tPPCK9OyPpPM/IU0+Nz9zAgAAAAjMiF8IYq21kuxA+40xNxljNhhjNhw4cGCk0wWiqzehp14/pOXzJsjk6wrW72+TojXSin/Jz3wAAAAAAjXccLbfGHOGJHnLtoE6Wmtvt9YuttYuHj9+/DCnC9bTbxxUT9zJ3/Nmr/xeeu1x6bIvSnXF+e8MAAAAwNAMN5w9IukGb/0GSQ9np5zC9MS2NtVUhHXBrPrcTxbvlR77ktQwR1pyU+7nAwAAAFAQBvMq/Z9JelrSPGPMLmPMjZK+JekKY8yrkt7hbZcka61WNbdp6exGVUbCuZ/w2R9Jh1+XrvyWFKnI/XwAAAAACkLkdB2stR8dYNflWa6lIG3f36E97d3628vn5H6yjv3uGxrnvEua847czwcAAACgYIz4hSClbmU+X6G/8qtSvFu68pu5nwsAAABAQSGcncaq5jYtnDxaE0dX5Xai3ZukzfdKF35Gajgzt3MBAAAAKDiEs1M42tmrjTuP5P4tjdZKv/uiVDteuvQfcjsXAAAAgIJ02mfOytnqVw7IsXm4pfGlB6Rd66WrfyhVjc7tXAAAAAAKElfOTmFVc5vqayt0ztSxuZuk57j0+L9Ik8+TzvlY7uYBAAAAUNC4cjaAhGO1+pUDWj5vgsIhk7uJ1n1P6tgrXXu3FCIrAwAAAOWKNDCA51uP6EhnTCvOyuEtjYdbpKd+IJ39YWnaktzNAwAAAKDgEc4G8MS2NoVDRpfMGZ+7SVZ9QwpFpHd8JXdzAAAAACgKhLMBrGxu0+IZ4zSmOpqbCU4ckrb+Sjr/emn05NzMAQAAAKBoEM4y2HO0S837OnL7Cv0X75OcmHT+J3I3BwAAAICiQTjLYNX2NknKXTizVtr8E2ny+dLEhbmZAwAAAEBRIZxlsKq5TVPHVWv2hLrcTLBnk9S2latmAAAAAPoQztJ0xxJ68rVDWjF/gozJ0Sv0N90jRaqlRdfkZnwAAAAARYdwluaZNw6pK5bQ8lzd0tjbKW35pbTgaqlqTG7mAAAAAFB0CGdpVjW3qToa1kWzGnIzwcsPSz3HuKURAAAAQD+EMx9rrVZub9PFsxtUFQ3nZpLN90j1s6QZF+dmfAAAAABFiXDm81rbcbUe7srdLY2HXpd2Pimd93EpV8+zAQAAAChKhDOflc3uK/SXz8tRONv8E8mEpHM+lpvxAQAAABQtwpnPyuY2zZ80SpPHVmd/8ERcev6n0px3SqPPyP74AAAAAIoa4czT3hXThp1HcvfD06/9UTq+z72lEQAAAADSEM48a189oIRjcxfONt8j1Y6X5l6Zm/EBAAAAFDXCmWdlc5vG1kR13vRx2R/8eJv0ymPSOR+RwtHsjw8AAACg6BHOJDmO1ertB7Rs7niFQzl4i+ILP5ecuHTe9dkfGwAAAEBJIJxJemHXUR060ZubV+hb697SOO0Cafzc7I8PAAAAoCQQziStam5TyEiXzR2f/cFb10sHX5HO+0T2xwYAAABQMghnkp5obtNbZ4zT2JqK7A+++W4pWistfH/2xwYAAABQMso+nO0/1q2te47l5pbGng5py0PSog9IlaOyPz4AAACAklH24WxVc5sk5eYV+lt/JcVO8CIQAAAAAKdV9uFsZXObJo+p0ryJObiytfkeqXGuNG1J9scGAAAAUFIiQRcQtMVN47S4aZyMyfIr9A9sl1qfla74mpTtsQEAAACUnLIPZzddemZuBt58jxSKuD88DQAAAACnUfa3NeZEIub+8PTcK6W6HDzLBgAAAKDkEM5y4ZXHpBMH+G0zAAAAAINGOMuFzT+R6iZJs98RdCUAAAAAigThLNuO7ZVe/YN07sekcNk/0gcAAABgkAhn2fbCTyXrSOd9POhKAAAAABQRwlk2Weve0jhjqdSQo7dAAgAAAChJhLNs2vmkdPgNrpoBAAAAGDLCWTZtukeqHC0tuDroSgAAAAAUGcJZtnS3Sy8/LC26RqqoCboaAAAAAEWGcJYtW34pxbuk8/ltMwAAAABDRzjLlk33SBMWSpPPD7oSAAAAAEWIcJYN+7dKeza5V82MCboaAAAAAEWIcJYNm+6RQlHpLdcGXQkAAACAIkU4G6l4j/Tiz6X575FqG4KuBgAAAECRIpyN1PbfSl1HeBEIAAAAgBEhnI3Upnuk0VOlWcuDrgQAAABAESOcjUT7bun1ldJ510mhcNDVAAAAAChikZEcbIzZIalDUkJS3Fq7OBtFFY3X/ijJuj88DQAAAAAjMKJw5llurT2YhXGKT8saqW6i1Dg36EoAAAAAFDluaxwua91wNvNSftsMAAAAwIiNNJxZSX8wxmw0xtyUjYKKxoHt0ok2N5wBAAAAwAiN9LbGpdba3caYCZIeN8Y0W2vX+Dt4oe0mSZo+ffoIpysgO9a6S8IZAAAAgCwY0ZUza+1ub9km6SFJSzL0ud1au9hau3j8+PEjma6wtKyWxkyXxjUFXQkAAACAEjDscGaMqTXGjEquS3qnpC3ZKqygOY60Yx1XzQAAAABkzUhua5wo6SHjvgwjIumn1trHslJVodu/Reo6QjgDAAAAkDXDDmfW2jcknZPFWopHi/dY3cxLgq0DAAAAQMngVfrD0bJGapgtjZ4cdCUAAAAASgThbKgScWnnU9zSCAAAACCrCGdDtfd5qbeDcAYAAAAgqwhnQ9Wy2l028bwZAAAAgOwhnA1VyxppwkKptjHoSgAAAACUEMLZUMR7pDef4ZZGAAAAAFlHOBuKXRukeDev0AcAAACQdYSzoWhZI5mQNOPioCsBAAAAUGIIZ0PRskY64xypemzQlQAAAAAoMYSzwertlHY9x/NmAAAAAHKCcDZYrc9ITkxqIpwBAAAAyD7C2WC1rJFCEWn6hUFXAgAAAKAEEc4Gq2WNNGWxVFkXdCUAAAAAShDhbDC626U9m3mFPgAAAICcIZwNxs6nJevwMhAAAAAAOUM4G4yWNVK4Upq6JOhKAAAAAJQowtlg7FgjTb9AilYFXQkAAACAEkU4O53Ow9K+l3iFPgAAAICcIpydzo617pLnzQAAAADkEOHsdFrWSNFaacr5QVcCAAAAoIQRzk6nZa004+1SOBp0JQAAAABKGOHsVDr2SQe38/tmAAAAAHKOcHYqLTxvBgAAACA/CGen0rJaqhojTTo76EoAAAAAlDjC2ansWCvNWCqFwkFXAgAAAKDEEc4GcmSndGQHtzQCAAAAyAvC2UD4fTMAAAAAeUQ4G0jLWqmmUZpwVtCVAAAAACgDhLNMrHV/fHrmJZIxQVcDAAAAoAwQzjI59LrUsYdbGgEAAADkDeEsk5bV7nLmZcHWAQAAAKBsEM4y2bFWGjVZqp8VdCUAAAAAygThLJ3juC8DmXkpz5sBAAAAyBvCWboD26TOgzxvBgAAACCvCGfpWta4y5mXBFsHAAAAgLJCOEvXslYa1ySNnR50JQAAAADKCOHMz0lIO9ZxSyMAAACAvCOc+e19Qepp5xX6AAAAAPKOcOa3Y627bOJ5MwAAAAD5RTjza1kjNc6TRk0MuhIAAAAAZYZwlhTvlXY+zfNmAAAAAAJBOEvas0mKnSCcAQAAAAgE4SypZa0kIzUtDboSAAAAAGWIcJbUslqatEiqqQ+6EgAAAABliHAmSbFuqXU9r9AHAAAAEBjCmSTtWi8lenjeDAAAAEBgCGeS+wp9E5amXxR0JQAAAADKFOFMcsPZ5POkqtFBVwIAAACgTI0onBljrjTGbDfGvGaMuTVbReVVz3Fp90ZuaQQAAAAQqGGHM2NMWNIPJV0laYGkjxpjFmSrsLx58xnJiUszLwm6EgAAAABlbCRXzpZIes1a+4a1tlfSzyVdnZ2y8qhltRSKStMuDLoSAAAAAGVsJOFsiqRW3/Yur60fY8xNxpgNxpgNBw4cGMF0OdKyRpq2RKqoCboSAAAAAGUskusJrLW3S7pdkhYvXmxzPd+Qfew+qfNw0FUAAAAAKHMjCWe7JU3zbU/12orLqEnuBwAAAAACNJLbGp+TNMcYM9MYUyHpI5IeyU5ZAAAAAFBehn3lzFobN8Z8VtLvJYUl3Wmt3Zq1ygAAAACgjIzomTNr7W8l/TZLtQAAAABA2RrRj1ADAAAAALKDcAYAAAAABYBwBgAAAAAFgHAGAAAAAAWAcAYAAAAABYBwBgAAAAAFgHAGAAAAAAXAWGvzN5kxByTtzNuEg9co6WDQRaAscK4hnzjfkC+ca8gXzjXkSy7PtRnW2vGZduQ1nBUqY8wGa+3ioOtA6eNcQz5xviFfONeQL5xryJegzjVuawQAAACAAkA4AwAAAIACQDhz3R50ASgbnGvIJ8435AvnGvKFcw35Esi5xjNnAAAAAFAAuHIGAAAAAAWgrMOZMeZKY8x2Y8xrxphbg64HpcUYc6cxps0Ys8XXVm+MedwY86q3HBdkjSgNxphpxphVxpiXjTFbjTGf89o535BVxpgqY8x6Y8wL3rn2r177TGPMs97f0/uMMRVB14rSYIwJG2M2G2N+7W1zriEnjDE7jDEvGWOeN8Zs8Nry/ne0bMOZMSYs6YeSrpK0QNJHjTELgq0KJebHkq5Ma7tV0hPW2jmSnvC2gZGKS7rFWrtA0oWS/tr7/zPON2Rbj6QV1tpzJJ0r6UpjzIWSvi3pe9ba2ZKOSLoxuBJRYj4naZtvm3MNubTcWnuu7xX6ef87WrbhTNISSa9Za9+w1vZK+rmkqwOuCSXEWrtG0uG05qsl3eWt3yXp/fmsCaXJWrvXWrvJW++Q+0VmijjfkGXWddzbjHofK2mFpF947ZxryApjzFRJ75H0n962Eeca8ivvf0fLOZxNkdTq297ltQG5NNFau9db3ydpYpDFoPQYY5oknSfpWXG+IQe828yel9Qm6XFJr0s6aq2Ne134e4ps+b6kL0hyvO0Gca4hd6ykPxhjNhpjbvLa8v53NJLrCQBkZq21xhhel4qsMcbUSfqlpJuttcfc/8js4nxDtlhrE5LONcaMlfSQpPnBVoRSZIx5r6Q2a+1GY8yygMtBeVhqrd1tjJkg6XFjTLN/Z77+jpbzlbPdkqb5tqd6bUAu7TfGnCFJ3rIt4HpQIowxUbnB7F5r7YNeM+cbcsZae1TSKkkXSRprjEn+B1/+niIbLpb0Z8aYHXIfPVkh6d/FuYYcsdbu9pZtcv/D0xIF8He0nMPZc5LmeG/9qZD0EUmPBFwTSt8jkm7w1m+Q9HCAtaBEeM9h3CFpm7X2u75dnG/IKmPMeO+KmYwx1ZKukPuM4ypJH/S6ca5hxKy1X7LWTrXWNsn9jrbSWnudONeQA8aYWmPMqOS6pHdK2qIA/o6W9Y9QG2PeLfd+5rCkO6213wi2IpQSY8zPJC2T1Chpv6QvS/qVpPslTZe0U9K11tr0l4YAQ2KMWSppraSXlHo24za5z51xviFrjDFny30oPiz3P/Deb639qjFmltyrG/WSNkv6uLW2J7hKUUq82xo/b619L+cacsE7rx7yNiOSfmqt/YYxpkF5/jta1uEMAAAAAApFOd/WCAAAAAAFg3AGAAAAAAWAcAYAAAAABYBwBgAAAAAFgHAGAAAAAAWAcAYAAAAABYBwBgAAAAAFgHAGAAAAAAXg/wP5expgcua/zwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Q_vals_1[:,0])\n",
    "plt.plot(Q_vals_1[:,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "numeric-prize",
   "metadata": {},
   "source": [
    "For Q-learning we do a simple example here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "operational-japan",
   "metadata": {},
   "outputs": [],
   "source": [
    "def step(state,action):\n",
    "    probas = transition_probabilities[state][action]\n",
    "    next_state = np.random.choice([0,1,2],p=probas)\n",
    "    reward = rewards[state][action][next_state]\n",
    "    return next_state,reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "sharp-scholarship",
   "metadata": {},
   "outputs": [],
   "source": [
    "def exploration_policy(state):\n",
    "    return np.random.choice(possible_actions[state])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "rising-patient",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_values = np.full((3, 3), -np.inf) # -np.inf for impossible actions \n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0 # for all possible actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "weighted-harrison",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha0 = 0.05 # initial learning rate\n",
    "decay = 0.005 # learning rate decay\n",
    "gamma = 0.95 # discount factor\n",
    "state =0 # initial state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "functioning-commonwealth",
   "metadata": {},
   "outputs": [],
   "source": [
    "Qt_vals_1=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "developmental-adult",
   "metadata": {},
   "outputs": [],
   "source": [
    "for iteration in range(100000):\n",
    "    action = exploration_policy(state)\n",
    "    next_state,reward  = step(state,action)\n",
    "    next_value = np.max(Q_values[next_state])\n",
    "    alpha = alpha0/(1+iteration*decay)\n",
    "    Q_values[state,action] *= 1-alpha\n",
    "    Q_values[state,action]  += alpha * (reward + gamma* next_value)\n",
    "    state = next_state\n",
    "    Qt_vals_1.append(Q_values[1].copy())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "global-championship",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20.49641143, 19.40960142, 15.57212179],\n",
       "       [ 0.        ,        -inf, -0.78999363],\n",
       "       [       -inf, 52.58488887,        -inf]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "vocational-automation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values.argmax(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "homeless-matter",
   "metadata": {},
   "outputs": [],
   "source": [
    "Qt_vals_1=np.array(Qt_vals_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "acoustic-volume",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcd189e0970>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Qt_vals_1[20:,0])\n",
    "plt.plot(Qt_vals_1[20:,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "arctic-retention",
   "metadata": {},
   "source": [
    "# Deep Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "marine-youth",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v0\")\n",
    "input_shape = [4] # == env.observation_space.shape \n",
    "n_outputs = 2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "checked-buyer",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    \n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.model=nn.Sequential(\n",
    "            nn.Linear(4,32),\n",
    "            nn.ELU(),\n",
    "            nn.Linear(32,32),\n",
    "            nn.ELU(),\n",
    "            nn.Linear(32,n_outputs)\n",
    "        )\n",
    "        \n",
    "    def forward(self,x):\n",
    "        if isinstance(x,np.ndarray):\n",
    "            x=torch.tensor(x)\n",
    "        return self.model(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "indonesian-naples",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "designed-paste",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05472796, 0.6168405 , 0.04615219, 0.91786397], dtype=float32)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state=np.random.uniform(0,1,4).astype(np.float32)\n",
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "trained-treat",
   "metadata": {},
   "outputs": [],
   "source": [
    "def epsilon_greedy_policy(state, epsilon=0): \n",
    "    if torch.rand(1) < epsilon:\n",
    "        return torch.randint(2,(1,))[0]\n",
    "    else:\n",
    "        with torch.no_grad():\n",
    "            Q_values = model(state[np.newaxis]) \n",
    "        return torch.argmax(Q_values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "acquired-pharmaceutical",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque \n",
    "replay_buffer = deque(maxlen=2000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "handy-beauty",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_experiences(batch_size):\n",
    "    indices = np.random.randint(len(replay_buffer), size=batch_size)\n",
    "    batch = [replay_buffer[index] for index in indices]\n",
    "    states, actions, rewards, next_states, dones = [\n",
    "            np.array([experience[field_index] for experience in batch])\n",
    "            for field_index in range(5)]\n",
    "    dones = torch.tensor(dones).type(torch.int)\n",
    "    rewards= torch.tensor(rewards).type(torch.float32)\n",
    "    actions=torch.tensor(actions)\n",
    "    return states, actions, rewards, next_states, dones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "flying-wrapping",
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_one_step(env, state, epsilon):\n",
    "    action = epsilon_greedy_policy(state, epsilon).numpy()\n",
    "    next_state, reward, done, info = env.step(action) \n",
    "    replay_buffer.append((state, action, reward, next_state, done)) \n",
    "    return next_state, reward, done, info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "united-military",
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_step(batch_size):\n",
    "    experiences = sample_experiences(batch_size)\n",
    "    states, actions, rewards, next_states, dones =  experiences\n",
    "    with torch.no_grad():\n",
    "        next_Q_values = model(next_states)\n",
    "    max_next_Q_values = torch.max(next_Q_values, axis=1).values\n",
    "    target_Q_values = (rewards +\n",
    "                           (1 - dones) * discount_factor * max_next_Q_values)\n",
    "    mask = torch.nn.functional.one_hot(actions, n_outputs)\n",
    "    all_Q_values = model(states)\n",
    "    Q_values = torch.sum(all_Q_values*mask,1)\n",
    "    loss =  loss_fn(Q_values,target_Q_values)\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "deluxe-incentive",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 32\n",
    "discount_factor = 0.95\n",
    "optimizer = torch.optim.Adam(model.parameters(),lr=1e-3)\n",
    "loss_fn=torch.nn.MSELoss()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "graphic-sheffield",
   "metadata": {},
   "outputs": [],
   "source": [
    "total_rewards=[]\n",
    "for episode in range(600):\n",
    "    obs = env.reset()\n",
    "    for step in range(200):\n",
    "        epsilon = max(1 - episode / 500, 0.01)\n",
    "        obs, reward, done, info = play_one_step(env, obs, epsilon)\n",
    "        if done:\n",
    "            break\n",
    "    total_rewards.append(step+1)\n",
    "    if episode > 50:\n",
    "            training_step(batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "running-birth",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcca8677cd0>]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(total_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "short-cargo",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "surprising-plaintiff",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}