LSPI_gym_interface_A_final.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MAbHFW9Ppr6I",
        "outputId": "2d989773-7f3b-4197-cb0a-2afcbac2654c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Starting virtual X frame buffer: Xvfb.\n"
          ]
        }
      ],
      "source": [
        "import sys, os\n",
        "if 'google.colab' in sys.modules and not os.path.exists('.setup_complete'):\n",
        "    !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/master/setup_colab.sh -O- | bash\n",
        "\n",
        "    !touch .setup_complete\n",
        "\n",
        "# This code creates a virtual display to draw game images on.\n",
        "# It will have no effect if your machine has a monitor.\n",
        "if type(os.environ.get(\"DISPLAY\")) is not str or len(os.environ.get(\"DISPLAY\")) == 0:\n",
        "    !bash ../xvfb start\n",
        "    os.environ['DISPLAY'] = ':1'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "7hsYfl6Jpr6Z"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SoxoILsDpr6a"
      },
      "source": [
        "### OpenAI Gym\n",
        "\n",
        "We're gonna spend several next weeks learning algorithms that solve decision processes. We are then in need of some interesting decision problems to test our algorithms.\n",
        "\n",
        "That's where OpenAI Gym comes into play. It's a Python library that wraps many classical decision problems including robot control, videogames and board games.\n",
        "\n",
        "So here's how it works:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZbFjUu8FTyIf"
      },
      "outputs": [],
      "source": [
        "#!pip3 install pyglet"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "S9NRmm1Ypr6b",
        "outputId": "855b93da-befd-41c8-8dfc-180fda1029bc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Observation space: Box(-1.2000000476837158, 0.6000000238418579, (2,), float32)\n",
            "Action space: Discrete(3)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import gym\n",
        "\n",
        "env = gym.make(\"MountainCar-v0\")\n",
        "env.reset()\n",
        "obs_array=env.render('rgb_array')\n",
        "plt.imshow(env.render('rgb_array'))\n",
        "print(\"Observation space:\", env.observation_space)\n",
        "print(\"Action space:\", env.action_space)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "KwWR51v7ROfF",
        "outputId": "c6e332cc-25f2-490b-ad7f-7ed5fbbe89b9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(400, 600)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f302e7a6c90>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "obs_array.shape\n",
        "# convert to grey scale\n",
        "def rgb2gray(rgb):\n",
        "\n",
        "    r, g, b = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2]\n",
        "    gray = 0.2989 * r + 0.5870 * g + 0.1140 * b\n",
        "\n",
        "    return gray\n",
        "print(rgb2gray(obs_array).shape)\n",
        "plt.imshow(rgb2gray(obs_array),cmap='Dark2')\n",
        "\n",
        "# from PIL import Image\n",
        "# img = Image.open('input_file.jpg').convert('L')\n",
        "# img.save('output_file.jpg')\n",
        "# import cv2\n",
        "# import numpy as np\n",
        "\n",
        "# img = cv2.imread('your_image.jpg')\n",
        "# res = cv2.resize(img, dsize=(54, 140), interpolation=cv2.INTER_CUBIC)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "N33QjcsDURsf",
        "outputId": "2a46d489-5286-46ca-9488-811327d605dc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f302e1f7b50>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import cv2\n",
        "img_grey=rgb2gray(obs_array)\n",
        "res = cv2.resize(img_grey, dsize=(300, 200), interpolation=cv2.INTER_CUBIC)\n",
        "plt.imshow(res,cmap='binary')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Agent making actions\n"
      ],
      "metadata": {
        "id": "ogqFSwf8Vuxn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "class Agent:\n",
        "    def __init__(self, env, preprocess_obs=None):\n",
        "        if preprocess_obs is None:\n",
        "            preprocess_obs = lambda x: x\n",
        "\n",
        "        self.env = env\n",
        "        self.action_size = self.env.action_space.n\n",
        "    \n",
        "    def set_Fhat(self, F_hat):\n",
        "        self.F_hat=F_hat\n",
        "\n",
        "    def set_features_size(self, k):\n",
        "        self.features_size = k\n",
        "        self.init_weights()\n",
        "\n",
        "    def init_weights(self, scale=1.):\n",
        "        size = self.features_size * self.action_size\n",
        "        self.weights = np.random.normal(size=size, scale=scale).reshape(self.features_size, self.action_size)\n",
        "\n",
        "    def set_weights(self, weights):\n",
        "        #k by n_actions\n",
        "        self.weights = weights\n",
        "\n",
        "    def get_features_size(self):\n",
        "        obs = self.env.observation_space.sample()\n",
        "        features = self.get_features(obs)\n",
        "        return len(features)\n",
        "\n",
        "\n",
        "    def get_features(self, obs):\n",
        "        # may flatten observations\n",
        "        #shape 1 by k\n",
        "        return obs@self.F_hat\n",
        "\n",
        "    def predict(self, obs):\n",
        "        values = self.get_features(obs)@self.weights\n",
        "        # values = np.dot(\n",
        "        #     self.weights.reshape(self.action_size, self.features_size),\n",
        "        #     obs)\n",
        "        action = np.argmax(values)\n",
        "        return action"
      ],
      "metadata": {
        "id": "Ns6x3rMeVzJ8"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "aaaaaa=dict()\n",
        "aaaaaa[0]=[1,2,3,3]\n",
        "aaaaaa[1]=[1,2,3,3]\n",
        "aaaaaa.items()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "viBptwPMeiU-",
        "outputId": "c182644a-d832-450e-c2c6-16eb0fa6d164"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_items([(0, [1, 2, 3, 3]), (1, [1, 2, 3, 3])])"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nep7MokOntEX"
      },
      "source": [
        "Simulate states, actions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "kPm2JGwnnW1q"
      },
      "outputs": [],
      "source": [
        "from IPython import display\n",
        "\n",
        "# Create env manually to set time limit. Please don't change this.\n",
        "TIME_LIMIT = 250\n",
        "env = gym.wrappers.TimeLimit(\n",
        "    gym.envs.classic_control.MountainCarEnv(),\n",
        "    max_episode_steps=TIME_LIMIT + 1,\n",
        ")\n",
        "actions = {'left': 0, 'stop': 1, 'right': 2}\n",
        "def policy(obs, t):\n",
        "    # Write the code for your policy here. You can use the observation\n",
        "    # (a tuple of position and velocity), the current time step, or both,\n",
        "    # if you want.\n",
        "    position, velocity = obs\n",
        "    if velocity<0:\n",
        "        return actions['left']\n",
        "    else:\n",
        "        return actions['right']  \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "prRCYn55m1OT",
        "outputId": "8b71ecb3-4b52-4241-e934-956f651e0c11"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "state_img2_sequence=[]\n",
        "action_sequence=[]\n",
        "reward_seqeunce=[]\n",
        "TIME_LIMIT=1000\n",
        "obs = env.reset()\n",
        "obs_array=env.render('rgb_array')\n",
        "img_grey=rgb2gray(obs_array)\n",
        "res = cv2.resize(img_grey, dsize=(150, 100), interpolation=cv2.INTER_CUBIC)\n",
        "plt.imshow(res)\n",
        "prev_state_img = res\n",
        "#plt.savefig('/content/drive/MyDrive/RL_proj_car_images/car_img_iter'+str(0)+'.png')\n",
        "\n",
        "\n",
        "##\n",
        "\n",
        "action = policy(obs, 0)  # Call your policy\n",
        "obs, reward, done, _ = env.step(action)\n",
        "obs_array=env.render('rgb_array')\n",
        "img_grey=rgb2gray(obs_array)\n",
        "res = cv2.resize(img_grey, dsize=(150, 100), interpolation=cv2.INTER_CUBIC)\n",
        "    #make a tensor of 2 pictures to incorporate velocity tensor\n",
        "state_img2=np.zeros([prev_state_img.shape[0],prev_state_img.shape[1],2])\n",
        "state_img2[:,:,0] = prev_state_img\n",
        "state_img2[:,:,1] = res\n",
        "\n",
        "    # saving more wisely  is desired\n",
        "    #flatten\n",
        "state_img2_sequence.append(state_img2.flatten())\n",
        "for t in range(1, TIME_LIMIT):\n",
        "    plt.gca().clear()\n",
        "    \n",
        "    #agent.predict(obs)\n",
        "    action = policy(obs, t)  # Call your policy\n",
        "    obs, reward, done, _ = env.step(action)  # Pass the action chosen by the policy to the environment\n",
        "    \n",
        "    action_sequence.append(action)\n",
        "    reward_seqeunce.append(reward)\n",
        "    # We don't do anything with reward here because MountainCar is a very simple environment,\n",
        "    # and reward is a constant -1. Therefore, your goal is to end the episode as quickly as possible.\n",
        "\n",
        "    # Draw game image on display.\n",
        "    obs_array=env.render('rgb_array')\n",
        "    img_grey=rgb2gray(obs_array)\n",
        "    res = cv2.resize(img_grey, dsize=(150, 100), interpolation=cv2.INTER_CUBIC)\n",
        "\n",
        "    #make a tensor of 2 pictures to incorporate velocity tensor\n",
        "    state_img2=np.zeros([prev_state_img.shape[0],prev_state_img.shape[1],2])\n",
        "    #flatten at this stage\n",
        "    state_img2[:,:,0] = prev_state_img\n",
        "    state_img2[:,:,1] = res\n",
        "    # saving more wisely  is desired\n",
        "    state_img2_sequence.append(state_img2.flatten())\n",
        "\n",
        "    #visualisation\n",
        "    plt.imshow(res)\n",
        "    #plt.savefig('/content/drive/MyDrive/RL_proj_car_images/car_img_iter'+str(t)+'.png')\n",
        "    display.display(plt.gcf())\n",
        "    display.clear_output(wait=True)\n",
        "\n",
        "    #next state:\n",
        "    prev_state_img = res.copy()\n",
        "    if done:\n",
        "        print(\"Well done!\")\n",
        "        break\n",
        "else:\n",
        "    print(\"Time limit exceeded. Try again.\")\n",
        "\n",
        "display.clear_output(wait=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "vWm1jbLm3clH"
      },
      "outputs": [],
      "source": [
        "Actions_set=[0,1,2]\n",
        "\n",
        "def make_A(action_sequence, reward_seqeunce, state_img2_sequence):\n",
        "    action_sequence=np.array(action_sequence)\n",
        "    state_img2_sequence=np.array(state_img2_sequence)\n",
        "    reward_seqeunce=np.array(reward_seqeunce)\n",
        "    feature_dict_action={}\n",
        "    feature_next_action={}\n",
        "    reward_action_dict={}\n",
        "    for action in Actions_set:\n",
        "        indices=np.arange(len(action_sequence))\n",
        "        #print(action_sequence)\n",
        "        indices_act=indices[action_sequence==action]\n",
        "        #print(indices_act)\n",
        "        features = state_img2_sequence[indices_act]\n",
        "\n",
        "        #print(features.shape)\n",
        "        features_next = state_img2_sequence[indices_act]\n",
        "        #[1:][action_sequence==action]\n",
        "        #print(features_next.shape)\n",
        "        rewards_a=reward_seqeunce[action_sequence==action]\n",
        "\n",
        "\n",
        "        feature_dict_action[action]=features\n",
        "        feature_next_action[action]=features_next\n",
        "        reward_action_dict[action] = rewards_a\n",
        "\n",
        "\n",
        "\n",
        "    return feature_dict_action, feature_next_action, reward_action_dict\n",
        "\n",
        "feature_dict_action, feature_next_action, reward_action_dict = make_A(action_sequence, reward_seqeunce, state_img2_sequence)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "rhQorW-cjnZm"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import scipy.linalg as la\n",
        "from sklearn.utils.extmath import randomized_svd\n",
        "\n",
        "\n",
        "\n",
        "def calculate_weights(gamma, P_F, r_F):\n",
        "    '''\n",
        "    gamma : scalar\n",
        "           discounted infinite-horizon return\n",
        "    P_F : matrix k x k\n",
        "    r_F: vector k\n",
        "        r_F from r_A = F^(+) @  r_A @ F\n",
        "    Return : weights k\n",
        "             r_F + gamma * inverse(I_k - gamma * v @ US) @ (V @ r_F)\n",
        "    '''\n",
        "    \n",
        "    l = US.shape[0]\n",
        "    k = US.shape[1]\n",
        "    I_k = np.eye(k)\n",
        "    \n",
        "#    return r_F + gamma * (US @ (np.linalg.inv(I_k - gamma * V @ US) @ (V @ r_F))) \n",
        "    return np.linalg.inv(I_k - gamma * P_F) @ r_F\n",
        "\n",
        "\n",
        "\n",
        "def calculate_r_F(F, r_A):\n",
        "    '''\n",
        "    F : matrix n x k\n",
        "        V from SVD(Prob_trans)\n",
        "    r_A: vector L\n",
        "        r_A = A^(+) @ rewards\n",
        "        \n",
        "    Return : r_F: vector k\n",
        "        r_F from r_A = np.linalg.pinv(F) @  r_A @ F\n",
        "    '''\n",
        "    \n",
        "    return np.linalg.pinv(F) @ r_A\n",
        "    \n",
        "\n",
        "    \n",
        "def get_features_matrix_hat(P_A, r_A):\n",
        "    '''\n",
        "    P_A : matrix l x l\n",
        "        matrix transition probabilities\n",
        "    r_A : vector l\n",
        "        compressed reward vector \n",
        "        \n",
        "    Return : F_hat : feature matrix for P_A\n",
        "        see return algorithm 2 from article\n",
        "    '''\n",
        "    \n",
        "    U, S, V_T = randomized_svd(M=P_A, n_components=k, n_iter=5)\n",
        "    l = U.shape[0]\n",
        "    \n",
        "    F_hat = np.append(U[:, :(k - 1)], r_A.reshape(l, 1), axis=1)\n",
        "    \n",
        "    US = U @ S\n",
        "    US = U * S.reshape(1, -1)\n",
        "     \n",
        "    return F_hat, US, V_T.T\n",
        "\n",
        "    \n",
        "def get_features_matrix(P_A, r_A, A_current):\n",
        "    '''\n",
        "    P_A : matrix l x l\n",
        "        matrix transition probabilities\n",
        "    r_A : vector l\n",
        "        compressed reward vector \n",
        "        \n",
        "    A : matrix n x l\n",
        "        matrix for current state\n",
        "        \n",
        "    Return : F_hat : feature matrix for P_A\n",
        "        see return algorithm 2 from article\n",
        "    '''\n",
        "    F_hat, US, V = get_features_matrix_hat(P_A, r_A)\n",
        "    \n",
        "    return A_current @ F_hat, US, V\n",
        " \n",
        "\n",
        "def get_P_F(P_A, F_hat):\n",
        "    '''\n",
        "    P_A : matrix l x l\n",
        "        matrix transition probabilities\n",
        "    F: matrix l x k\n",
        "        feature matrix\n",
        "        \n",
        "    Return : P_F\n",
        "    '''\n",
        "    \n",
        "    \n",
        "    return np.linalg.pinv(F_hat) @ P_A @ F_hat\n",
        " \n",
        "\n",
        "\n",
        "\n",
        "\n",
        "def LRA(A, r, method='svd', max_iter=16):\n",
        "    if method=='svd':\n",
        "        U, s, V = la.svd(A)\n",
        "        return U[:,:r]*s[:r].reshape(1, -1), V[:r,:]\n",
        "    if method=='eigen':\n",
        "        w, vr = la.eig(A, right=True)\n",
        "        ind = np.argpartition(np.abs(w), w.shape[0]-r)[-r:]\n",
        "        return vr[:, ind]*w[ind], la.inv(vr)[ind, :]\n",
        "    if method=='lfd':\n",
        "        D = np.random.rand(r, A.shape[1])\n",
        "        E = np.random.rand(A.shape[1], r)\n",
        "        diff, i = np.inf, 0\n",
        "        while la.norm(E@D - A) < diff and i < max_iter:\n",
        "            diff = la.norm(E@D - A)\n",
        "            E = A @ la.pinv(D)\n",
        "            D = la.pinv(E) @ A\n",
        "            i += 1\n",
        "        return E, D\n",
        "    raise ValueError('Unidentified method')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.rand()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7drwIQbWt0WV",
        "outputId": "fc894a16-3fd1-4f06-9540-97f52433e5de"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.10150978278481071"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "qQN5GdwQTyIr"
      },
      "outputs": [],
      "source": [
        "import cv2\n",
        "\n",
        "\n",
        "def Sample_agent_policy(env, agent = None, is_agent = False):\n",
        "\n",
        "  actions = {'left': 0, 'stop': 1, 'right': 2}\n",
        "  def policy(obs, t):\n",
        "    # epsilon greedy\n",
        "    # Write the code for your policy here. You can use the observation\n",
        "    # (a tuple of position and velocity), the current time step, or both,\n",
        "    # if you want.\n",
        "    if np.random.rand()>0.8: \n",
        "      return np.random.choice(3)\n",
        "    else:\n",
        "      position, velocity = obs\n",
        "      if velocity<0:\n",
        "        return actions['left']\n",
        "      else:\n",
        "        return actions['right']  \n",
        "\n",
        "  def rgb2gray(rgb):\n",
        "\n",
        "    r, g, b = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2]\n",
        "    gray = 0.2989 * r + 0.5870 * g + 0.1140 * b\n",
        "\n",
        "    return gray\n",
        "  def grey_and_scale(img):\n",
        "#    return cv2.resize(rgb2gray(img), dsize=(150, 100), interpolation=cv2.INTER_CUBIC)\n",
        "    return cv2.resize(rgb2gray(img), dsize=(40, 60), interpolation=cv2.INTER_CUBIC)\n",
        "\n",
        "\n",
        "  state_img2_sequence=[]\n",
        "  action_sequence=[]\n",
        "  reward_seqeunce=[]\n",
        "  TIME_LIMIT=500\n",
        "  obs = env.reset()\n",
        "  obs_array=env.render('rgb_array')\n",
        "\n",
        "  res =grey_and_scale(obs_array)\n",
        "  plt.imshow(res)\n",
        "  prev_state_img = res\n",
        "\n",
        "  action = policy(obs, 0)  # Call your policy\n",
        "\n",
        "  obs, reward, done, _ = env.step(action)\n",
        "  obs_array=env.render('rgb_array')\n",
        "  res=grey_and_scale(obs_array)\n",
        "      #make a tensor of 2 pictures to incorporate velocity tensor\n",
        "  state_img2=np.zeros([prev_state_img.shape[0],prev_state_img.shape[1],2])\n",
        "  state_img2[:,:,0] = prev_state_img\n",
        "  state_img2[:,:,1] = res\n",
        "\n",
        "  # saving more wisely  is desired\n",
        "   #flatten\n",
        "  state_img2_sequence.append(state_img2.flatten())\n",
        "  for t in range(1, TIME_LIMIT):\n",
        "      plt.gca().clear()\n",
        "      \n",
        "      #agent.predict(obs)\n",
        "      if is_agent:\n",
        "        action = agent.predict(state_img2_sequence[-1])\n",
        "      else:\n",
        "        action = policy(obs, t)\n",
        "        # Call your policy\n",
        "      obs, reward, done, _ = env.step(action)  # Pass the action chosen by the policy to the environment\n",
        "      \n",
        "      action_sequence.append(action)\n",
        "      reward_seqeunce.append(reward)\n",
        "      # We don't do anything with reward here because MountainCar is a very simple environment,\n",
        "      # and reward is a constant -1. Therefore, your goal is to end the episode as quickly as possible.\n",
        "\n",
        "      # Draw game image on display.\n",
        "      obs_array=env.render('rgb_array')\n",
        "      res = grey_and_scale(obs_array)\n",
        "\n",
        "      #make a tensor of 2 pictures to incorporate velocity tensor\n",
        "      state_img2=np.zeros([prev_state_img.shape[0],prev_state_img.shape[1],2])\n",
        "      #flatten at this stage\n",
        "      state_img2[:,:,0] = prev_state_img\n",
        "      state_img2[:,:,1] = res\n",
        "      # saving more wisely  is desired\n",
        "      state_img2_sequence.append(state_img2.flatten())\n",
        "\n",
        "      #visualisation\n",
        "      plt.imshow(res)\n",
        "      \n",
        "      display.display(plt.gcf())\n",
        "      display.clear_output(wait=True)\n",
        "\n",
        "      #next state:\n",
        "      prev_state_img = res.copy()\n",
        "      if done:\n",
        "          print(\"Well done!\")\n",
        "          break\n",
        "  else:\n",
        "      print(\"Time limit exceeded. Try again.\")\n",
        "\n",
        "  display.clear_output(wait=True)\n",
        "  return state_img2_sequence, action_sequence, reward_seqeunce"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "id": "C6nVab_6fAGo",
        "outputId": "874ad429-f7f6-41ef-a6f5-73a73674b513",
        "scrolled": false
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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84pmi06g7D15vZlZyLgRmZiXnQmBmVnIuBGZmJedCYGZWci4EZmYl50JgZlZyLgRmZiXnDmVmVmof/fliXn50Ake+aQtvfdUvuWjyj5m3Zintaw8HPlN0enXhPQIzK6UuxM7uQ9BdE5n9961sazmSHz99DFNGHErD3RM4+m8eKDrFuvEegZmV0hfb5rPl88fw/Hs7aPr+y8wb/wOmj9zBI+27+OAf386jHzwSTik6y/pwITCz0hmrTsaP2MPmcQ0cOf0Z/uTIO36zbFeM4MzxD3Pm+If5VoE51pMLgZmVSoVgxogRfHHqf7D+f91Ng7qLTqlwLgRmVjpbutrpBkaqq+hUBoVMJ4slzZe0XlKrpIt7WX6FpAfTx2OSdlYt66pa1pxn8mZmB+KF7jFs6pzItu7R7OweVXQ6g0aWoSorwJXAu4DNwGpJzRGxbu86EfHpqvU/AZxY9RIvR8Sb8kvZzOzg/PEPz2f6D4Mz//Zuzhz/cNHpDBpZ9gjmAq0RsSEi2oEbgAX7WX8RcH0eyZmZ5UmHtfPC1ApjK3uKTmVQyXKOYCrwZNX0ZuAtva0oaQYwC7ijavYYSS1AJ3B5RPxrL9stBZYCHHXUUdkyNzM7QDeddjVdp4kKUXQqg0reHcoWAjdHRPUZmBkR0QScC/yDpGN6bhQRKyKiKSKaGhsbc07JzMruX547mQ99/U/58yfe7yLQiyyFoA2YXjU9LZ3Xm4X0OCwUEW3pzw3AXex7/sDMrOZaX2rkqFue45eb/UWzN1kODa0GZkuaRVIAFpJ8u9+HpOOAicDPquZNBHZFxB5Jk4FTgS/kkbiZWVbnv/pu7v/mTC4YvaXoVAalfgtBRHRKWgbcClSAlRGxVtJyoCUi9l4SuhC4ISKq97uOB66W1E2y93F59dVGZma11IX4Ytt8RjV08ekp/1F0OoNWpg5lEXELcEuPeX/VY/qve9nup8AbBpCfmdlB29U9mie+cSydY0XHJ293B7I+uGex2TAhaTrwDeBIIIAVEfGPkiYBNwIzgY3AByLi2aLyrKcx6mDKuRsZ1dDpW0nshwuB2fDRCXwmIu6XNB5YI+k24CPA7RFxeXpngIuBvygwz7oZqS7+54zvFZ3GoOfxCMyGiYh4KiLuT5+/ADxC0g9oAXBdutp1wDnFZGiDlQuB2TAkaSbJpdr3AkdGxFPpoqdJDh31ts1SSS2SWnbuGPrH0ldsezsfWvPHPNo+pehUBj0XArNhRtKhwHeBP42I56uXpVf19dqjqrpj54RJlTpkWlu3//i/MPPil7jnuWOLTmXQcyEwG0YkjSQpAt+KiH9OZ2+RNCVdPgXYWlR+9fS+313Fs/+ngXkT1hadyqDnk8Vmw4QkAdcAj0TEl6oWNQOLgcvTn/2ePe1GdERlyF5uWSFYNOFePjDhvqJTGRK8R2A2fJwKfAj43aoxQM4iKQDvkvQ4cEY6vV8vdI1h7Z6ptc22RioEo9VFg3xPoay8R2A2TETEfwLqY/E7D+S1RquTxhHP97/iILQ7RrCpcyKHNexmfMPuotMZErxHYGavMLahnWNGbi86jYPyUoxiza5ZtHVOLDqVIcN7BGb2CgF0xND8nji+YTdvHdfK2AYPPpPV0PxNm1lNBeKxjldx3fZTebJzUtHpZPZSjGJ3jKSx8gLj1F50OkOGC4GZ9eqSlt+n9YyxLH/kPUWnktn9L8/k/pdnFp3GkONCYGa9evOMX7Fx2QmcMuVXRaeSWXc00BFDvzNcvfkcgZn16jOvuRWW3Fp0GgekQd0wRM9tFCnTJyZpvqT1klrTuxf2XP4RSduqrl3+WNWyxZIeTx+L80zezKzam8Zs4qRDNhadxpDT7x6BpApwJfAuYDOwWlJzLyON3RgRy3psOwm4FGgiuRBhTbptKe6FbjYcfHdnE9s7xvHhyT9hjDqLTqdXHVHhpRjF+IbdHpz+IGTZI5gLtEbEhohoB24gua1tFmcCt0XEjvSf/23A/INL1cyKcPsVp7Jp6Sw2dgzegd83dU7iP198HS90jyk6lSEpSyGYCjxZNb05ndfT+yQ9JOnmdKSkzNtW3/5227ZtGVM3s3p49qyXWH/+eBorg7encXc00I3o8vmBg5LXyeLvA9dHxB5J/41k8IvfzbpxRKwAVgA0NTV5v85sELn+LV8vOoV+NaibBoKKh6M8KFnKZxswvWp6WjrvNyJie0Ts7cb3deDkrNuamQ3UUSN28PZDH/W9hQ5SlkKwGpgtaZakUcBCktva/sbee52nziYZIg/gVmCepImSJgLz0nlmNoRs7xrHZZt+j+/ubCo6lX10IbZ3jaOdik8UD0C/hSAiOoFlJP/AHwFuioi1kpZLOjtd7ZOS1kr6OfBJksGyiYgdwGUkxWQ1sDydZ2ZDyM9emk3HuRW+/+3Tik5lH7u6R/Ozl2azsX1y0akMaZnOEUTELcAtPeb9VdXzzwKf7WPblcDKAeRoZgU7/pA2rv0fpzF91lP9r1yAbt8kYUDcs9jM+nXMyG3cfOZXik7jFRrUTUXdNOCTxAPhQmBmQ9Y4tfO2Qx9lFENzSM3BwvtTZpbZj148gWWPLuLhPdOKToUKQYVgnNqH7NjKg4ULgZlldtVPT+fws59k5a9OLToVRqqbke43kAsXAjPL7PdOfpD1K97AOVN/XnQqPNp+JA/veU3RaQwLPkdgZpl9bPKPufAdd7MnKnShQnN5uvNw9nSP5OhRW91/YIBcCMwss4699/QpuAgAnDxmI13IRSAHPjRkZgekC3HJL3+fT65fyO6o/3fJl2IUbZ0TAAbtbbGHGhcCMzsgXYhdX57K+EsOYXvXoXWP/3Tn4azZNYud3WPrHnu48qEhs2EmHUyqBWiLiPdKmkUyjsgRwBrgQ+nYIgelQsCF29iyezRHVF7MJ+kDMHXEsxw2bjcTGnbVPfZw5UJgNvx8iuS+YIel058HroiIGyRdBSwBvjaQAFcce+PAMhyA8Q3tTGrYPShOWA8XPjRkNoxImga8h+R28EgSydggN6erXAecU0x2+eiIBheBnLkQmA0v/wD8Ofzm5jtHADvTuwhD3yMM7jNS4M4d/ffU3dgxmQ/f/1G+suWdOaTdv7bOCSy692P87ZPvcRHImQuB2TAh6b3A1ohYczDbR8SKiGiKiKYJkyr9rr/qxWOY8Zd7+Mkdrz+YcAfsgV0zee2nnqb1e7PrEq9MfI7AbPg4FThb0lnAGJJzBP8ITJA0It0ryG2UwN8Zv56f/uMszmpcncfL9atp3Ab+7ZrX8+bJD9UlXpm4EJgNE9Xjgkg6HfiziPgjSd8B3k9y5dBi4Ht5xJs6Yidfft0NebxUJq+uPM9VJ/y/usUrk0yHhiTNl7ReUquki3tZfpGkdZIeknS7pBlVy7okPZg+mntua2Y19xfARZJaSc4ZXFNwPjbI9FsI0muSrwTeDcwBFkma02O1B4CmiHgjydUJX6ha9nJEvCl9nI2Z1VxE3BUR702fb4iIuRHx2oj4w4jYk2esq7a+gz+85wJWvzwrz5fdx6cf+yDntSzhhe4xNYtRZln2COYCrWljaifZvVxQvUJE3BkRe3t3rCI5DmlmJfCj+0/g+M9t5Y4dx9Usxov/8mqmfWUET3ceXrMYZZalEEwFnqya7vPys9QS4AdV02PSS9JWSer1+uXqy9a2bduWISUzGywuOO1O2q8V739VS81inLLkAcZftpnpI7fXLEaZ5XqyWNJ5QBPw9qrZMyKiTdLRwB2SHo6IJ6q3i4gVwAqApqYm30rQbAg549C1nHHoWp7oaOTx9iOZPWpLbq9dIRitLpZOvtt9B2ooyx5BGzC9arrXy88knQFcApxdfQwyItrSnxuAu4ATB5CvmQ1CXYjP3b+Az61ZQEf03wchq8MbOjh+1FjGN3Tk9pr2SlkKwWpgtqRZkkYBC4F9rv6RdCJwNUkR2Fo1f6Kk0enzySTXOa/LK3kzGzzmHrWJphmbaDjI4SMrBCPVvc/4Arujga1dL9Ee7vtaS/0eGoqITknLgFuBCrAyItZKWg60REQz8HfAocB3klubsCm9Quh44GpJ3SRF5/KIcCEwG2YqBJ+e8h8Deo0uBME+h4B2xQh2eciBmst0jiAibgFu6THvr6qen9HHdj8F3jCQBM2sHC791QKe/eoMRp3/FF987XeKTqdUvL9lZrmpEIxVJyMP4PDQ7hjBddtPZe2j05nw4408vfMwOqLCmt0zeaKjsYbZ2l4uBGaWm9Hq4tiRY2hsyH48Z2NHI+v++xuY8zdtxEu76OoSW7vG87/veQ9ffHxeDbO1vXyvITPLTQcNbO3axYbOsWzsaGTmyG37HVf4Lzf8AY8/MpXXbX+O7smH8/x/nc6MxjaOqLzIm0/YwKxx7jdQDy4EZpabjmjg112j2NjRSOvuI5k64tn9FoLWn09j5g870cvtvHzMETz9VjhnQhuTGnbzl1Nvcd+BOnEhMLPczRy5jakjnmVsw/5va3TR/H/nwVOP4u473kjSVcD9SYvgcwRmlrsx6mRswx6u2fY2/u8zv9Pneqcc8gR/eMR9dEzupHsUHLKlgS17DqPbewJ15UJgZjXxQvcYHvnbN7DmihMz9TY+5Ckx41ubuP/X09jtMYnryoXAzGpijDrY+kcvs+WUYMnXP8GfP/H+Xtd7ofsQGv9zBCN3Bes+N4X3HL22zpmaC4GZ1cQYdfKtN1/DnDduYsY/Pc4v176Gts4JdCEqBBWCnd2HsKG9kUkPPQ/AzfOuZOHEewvOvHxcCMysppZNu4Pjf7idES+JL/7ZeWxofxXHjhTHjhRLv38+/3bxOxlxxQ7O/dStRadaWi4EZlZTjZUXOHfSKrqm7+bFKRVGqosOkkf34R28ML3C7x/5AG8f92jRqZaWLx81s7q46bSr6TotOSzU2pGcPL759K/Rdbr2ueOo1Z/3CMysbnr7h+8iUDwXAjOzknMhMDMrORcCM7OSy1QIJM2XtF5Sq6SLe1k+WtKN6fJ7Jc2sWvbZdP56SWfml7qZmeWh30IgqQJcCbwbmAMskjSnx2pLgGcj4rXAFcDn023nkIxxfAIwH/hq+npmZjZIZNkjmAu0RsSGiGgHbgAW9FhnAXBd+vxm4J1KBi9eANwQEXsi4pdAa/p6ZmY2SGTpRzAVeLJqejPwlr7WSQe7fw44Ip2/qse2U3sGkLQUWJpO7pH0i0zZ528y8EyJ4hYZu8j3/LqC4g4Zjz7c/szcmZteorjf0V5FthOAGQXGrptB0aEsIlYAKwAktUREUxF5FBXb77n+sYuIO5RERGORv6O9BkMOZZDl0FAbML1qelo6r9d1JI0ADge2Z9zWzMwKlKUQrAZmS5olaRTJyd/mHus0A4vT5+8H7oiISOcvTK8qmgXMBu7LJ3UzM8tDv4eG0mP+y4BbgQqwMiLWSloOtEREM3AN8E1JrcAOkmJBut5NwDqgE/h4RHT1E3LFwb+dASsqtt9zeWIPJYPhcxoMOQx7Sr64m5lZWblnsZlZybkQmJmVXGGFYCC3rahD7IskrZP0kKTbJeVyLXF/cavWe5+kkJTLZXNZ4kr6QPqe10r6dh5xs8SWdJSkOyU9kH7eZ+UUd6WkrX31SVHiy2leD0k6KY+4w0XWtppjvOlpO9jbBj+Vzp8k6TZJj6c/J9Y6l1KKiLo/SE46PwEcDYwCfg7M6bHOnwBXpc8XAjfWMfY7gLHp8wvziJ0lbrreeOAeko54TXV6v7OBB4CJ6fSr6vhZrwAuTJ/PATbmFPttwEnAL/pYfhbwA0DAKcC9ebfzofrI2lZzjjkFOCl9Ph54LG0PXwAuTudfDHy+6M9nOD6K2iMYyG0rah47Iu6MiF3p5CqS/g81j5u6jOReTbtziJk17vnAlRHxLEBEbK1j7AAOS58fDvw6j8ARcQ/JFWx9WQB8IxKrgAmSpuQRexjI2lZzExFPRcT96fMXgEdI7kJQ/X/gOuCcWuZRVkUVgt5uW9Hz1hP73LYC2HvbinrErraE5JtjzeOmhyemR8S/5xAvc1zgWOBYST+RtErS/DrG/mvgPEmbgVuAT+QUuz8H2g7KpNDPJj0MfCJwL3BkRDyVLnoaOLJeeZSJTxbvh6TzgCbg7+oQqwH4EvCZWo56CCkAAAHBSURBVMfqxQiSw0OnA4uAf5I0oU6xFwHXRsQ0ksM130w/CyshSYcC3wX+NCKer14WyfEhX+9eA0X9wQ3kthX1iI2kM4BLgLMjYk8d4o4HXg/cJWkjyXHr5hxOGGd5v5uB5ojoiOQusY+RFIaByhJ7CXATQET8DBhDcqOxWvPtT/pWyGcjaSRJEfhWRPxzOnvL3kN26c+8DltalaIKwUBuW1Hz2JJOBK4mKQJ5Nbz9xo2I5yJickTMjIiZJOcmzo6Igd4gLctn/a8kewNImkxyqGjDAONmjb0JeGca+3iSQrAth9j9aQY+nF49dArwXNUhiLLL8nvLVXr+7xrgkYj4UtWi6v8Di4Hv1TKP0irqLDXJYYDHSK5OuCSdt5zknx8k/xC+QzKGwX3A0XWM/SNgC/Bg+miuR9we695FDlcNZXy/IjkstQ54GFhYx896DvATkitTHgTm5RT3euApoINkj2cJcAFwQdV7vjLN6+G8Puvh8ujt91bjeKeRHPZ5qOrv7iyS84K3A4+nf5eTiv5shuPDt5gwMys5n5QzMys5FwIzs5JzITAzKzkXAjOzknMhMDMrORcCM7OScyEwMyu5/w+NjCkl3qsZzwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 4 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "#from scipy.sparse.linalg import svds\n",
        "\n",
        "\n",
        "from sklearn.decomposition import TruncatedSVD\n",
        "from sklearn.utils.extmath import randomized_svd\n",
        "from tqdm import tqdm\n",
        "#from scipy.sparse import csr_matrix\n",
        "\n",
        "k = 10\n",
        "\n",
        "Agent_lspi=Agent(env)\n",
        "Agent_lspi.set_features_size(k)\n",
        "gamma=0.9\n",
        "iterations=10\n",
        "\n",
        "for i in range(iterations):\n",
        "    # sample according policy predicted by updated weight for \n",
        "    # make_A\n",
        "    #get features and features_next\n",
        "    #rewards for each action\n",
        "    # A state_action1 state_action1 by n_features(40) 30000 full rank \n",
        "\n",
        "    # A@A.T  state_action1 by state_action1 40 by 40\n",
        "    #A_next state_action1 by n_features\n",
        "    #for each action\n",
        "    \n",
        "    if (i==0):\n",
        "        print(\"hello world\")\n",
        "        state_img2_sequence, action_sequence, reward_seqeunce = Sample_agent_policy(env, agent=None, is_agent=False)\n",
        "    else:\n",
        "        state_img2_sequence, action_sequence, reward_seqeunce = Sample_agent_policy(env, agent=Agent_lspi, is_agent=True)\n",
        "    \n",
        "\n",
        "    feature_dict_action, feature_next_action,\\\n",
        "    reward_action_dict = make_A(action_sequence,\n",
        "                               reward_seqeunce, state_img2_sequence)\n",
        "  \n",
        "\n",
        "    fig, axs = plt.subplots(nrows=2, ncols=2) \n",
        "  #A_current, A_next , reward_A = make_A(action_sequence, reward_seqeunce, state_img2_sequence)\n",
        "    weights_action_list=[]\n",
        "    weigths_true_action_dict = {}\n",
        "    for action in tqdm(Actions_set):\n",
        "        if (feature_next_action[action].shape[0] == 0):\n",
        "            weights_action_list.append(np.random.rand(k))\n",
        "            continue\n",
        "            \n",
        "        A_next = feature_next_action[action]\n",
        "        A_current = feature_dict_action[action]\n",
        "        reward_A = reward_action_dict[action]\n",
        "        #inverse_moore = A_current.T@np.linalg.inv(A_current@A_current.T)\n",
        "        # A_current@inverse_moore = I\n",
        "        #state_action1 n_features\n",
        "        #np.pinv(A)\n",
        "        # n_features by n_features\n",
        "#        import pdb; pdb.set_trace()\n",
        "        Prob_A = la.pinv(A_current) @ A_next\n",
        "#        Prob_A = np.linalg.inv(A_current.T @ A_current) @ A_current.T @ A_next\n",
        "        print(\"Prob a\")\n",
        "        r_A =la.pinv(A_current) @ reward_A\n",
        "        print(\" r_A\")\n",
        "#        F_hat, US, V = get_features_matrix_hat(Prob_A, r_A)\n",
        "#        import pdb; pdb.set_trace()\n",
        "#        pdb.set_trace()\n",
        "        F, US, V = get_features_matrix(Prob_A, r_A, A_current)\n",
        "        F_hat, _ , _  = get_features_matrix_hat(Prob_A, r_A)\n",
        "        Agent_lspi.set_Fhat(F_hat)\n",
        "\n",
        "        print('LRA')\n",
        "\n",
        "        r_F = calculate_r_F(F, reward_A)\n",
        "        \n",
        "        P_F = get_P_F(Prob_A, F_hat)\n",
        "        weights_action = calculate_weights(gamma, P_F, r_F)\n",
        "        print(weights_action.shape)\n",
        "        print('weights_action')\n",
        "        \n",
        "        weigths_true_action_dict[action] = F_hat @ weights_action\n",
        "\n",
        "        weights_action_list.append(weights_action)\n",
        "        weights_true_action = F_hat @ weights_action \n",
        "        weights_true_action = weights_true_action.reshape(60, 40, 2)\n",
        "        if (action == 0):\n",
        "            axs[0, 0].imshow(weights_true_action[:,:,0])\n",
        "            axs[0, 0].set_title(\"Fig 1. Action left\")\n",
        "            axs[0, 1].imshow(weights_true_action[:,:,1])\n",
        "            axs[0, 1].set_title(\"Fig 2. Action left\")\n",
        "        if (action == 2):\n",
        "            axs[1, 0].imshow(weights_true_action[:,:,0])\n",
        "            axs[1, 0].set_title(\"Fig 1. Action right\")\n",
        "            axs[1, 1].imshow(weights_true_action[:,:,1])\n",
        "            axs[1, 1].set_title(\"Fig 2. Action right\")\n",
        "#        plt.imshow(weights_true_action[:,:,0])\n",
        "#        plt.imshow(weights_true_action[:,:])\n",
        "        #plot weights_action. cmap \n",
        "        #update policy according to new weights_action\n",
        "    weight_matrix = np.stack(weights_action_list)\n",
        "    print(weight_matrix.shape)\n",
        "    Agent_lspi.set_weights(weight_matrix.T)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "7Ffbbz18sMI8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bi0YmmN2TyIs"
      },
      "outputs": [],
      "source": [
        "np.sqrt(2000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zZBmzY9dTyIt",
        "outputId": "454aca9c-49f8-4e11-a6e1-f0e7b50e954c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0.04478354,  0.02909084,  0.03785851, ...,  0.01123415,\n",
              "         0.04183728,  0.00234701],\n",
              "       [ 0.00179641, -0.01342547, -0.00664226, ..., -0.00463774,\n",
              "        -0.00229532,  0.00213908],\n",
              "       [-0.02902286,  0.0675748 , -0.03355641, ...,  0.05730085,\n",
              "        -0.05403108,  0.01059323],\n",
              "       ...,\n",
              "       [ 0.03139422, -0.04301666,  0.0666454 , ..., -0.10459897,\n",
              "        -0.03851908,  0.00121881],\n",
              "       [ 0.02967128, -0.03230923,  0.08405059, ..., -0.0807908 ,\n",
              "        -0.04957663, -0.02846655],\n",
              "       [-0.01120274, -0.00017998, -0.05142193, ...,  0.03587175,\n",
              "         0.02111265, -0.00611361]])"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import numpy as np \n",
        "\n",
        "n = 3000\n",
        "A = np.random.random((n, n))\n",
        "np.linalg.pinv(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Zsn539iqTyIt",
        "outputId": "aea832a9-e966-4cbd-8616-0bab8d0570b5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [3 4 6]]\n"
          ]
        }
      ],
      "source": [
        "an_array = np.array([[1, 2], [3, 4]])\n",
        "\n",
        "\n",
        "new_column = [[3], [6]]\n",
        "\n",
        "an_array = np.append(an_array, new_column, axis=1)\n",
        "print(an_array)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fqsHb6_qxDTX"
      },
      "outputs": [],
      "source": [
        "print(V.shape)\n",
        "print(US.shape)\n",
        "del Prob_A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pC2h_B0aWWK4",
        "outputId": "886c2b47-4db2-41f9-def2-30b0e5049dd5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "LRA\n"
          ]
        }
      ],
      "source": [
        "#US=US*s.reshape(1, -1)\n",
        "    #US, V = LRA(Prob_A, r=100)\n",
        "print('LRA')\n",
        "    # weights_action optimization \n",
        "Inv_Woodbury = Woodbury(0.9, US, V)\n",
        "    \n",
        "weights_action=calculate_weights(Inv_Woodbury, r_A)\n",
        "weights_action_dict[action]=weights_action\n",
        "\n",
        "weights_action.reshape(150, 100, 2)\n",
        "plt.imshow(weights_action[:,:,0])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-HR-xUOFpr6c"
      },
      "source": [
        "Note: if you're running this on your local machine, you'll see a window pop up with the image above. Don't close it, just alt-tab away."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dhVwnwC6pr6c"
      },
      "source": [
        "### Gym interface\n",
        "\n",
        "The three main methods of an environment are\n",
        "* `reset()`: reset environment to the initial state, _return first observation_\n",
        "* `render()`: show current environment state (a more colorful version :) )\n",
        "* `step(a)`: commit action `a` and return `(new_observation, reward, is_done, info)`\n",
        " * `new_observation`: an observation right after committing the action `a`\n",
        " * `reward`: a number representing your reward for committing action `a`\n",
        " * `is_done`: True if the MDP has just finished, False if still in progress\n",
        " * `info`: some auxiliary stuff about what just happened. For now, ignore it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jNGnvU8Bpr6d",
        "outputId": "3975a586-5276-4f72-8003-9030fa43bfdb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "initial observation code: [-0.52586437  0.        ]\n"
          ]
        }
      ],
      "source": [
        "obs0 = env.reset()\n",
        "print(\"initial observation code:\", obs0)\n",
        "\n",
        "# Note: in MountainCar, observation is just two numbers: car position and velocity"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "re3YeRjRrAaI"
      },
      "outputs": [],
      "source": [
        "?np.append"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3PkqdVWbrp8t"
      },
      "source": [
        "Actions:\n",
        "1.   0 left\n",
        "2.   1 no step\n",
        "3.   2 right \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "odVbD1ZurEuZ"
      },
      "outputs": [],
      "source": [
        "?np.append\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 338
        },
        "id": "z8aRIzzXpr6e",
        "outputId": "977faa7d-0703-4715-90cf-5f35fc34bf88"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "taking action 2 (right)\n",
            "new observation code: [-0.55395261  0.00123657]\n",
            "reward: -1.0\n",
            "is game over?: False\n"
          ]
        },
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(\"taking action 2 (right)\")\n",
        "\n",
        "new_obs, reward, is_done, _ = env.step(2)\n",
        "                                       \n",
        "plt.imshow(env.render('rgb_array'))\n",
        "print(\"new observation code:\", new_obs)\n",
        "print(\"reward:\", reward)\n",
        "print(\"is game over?:\", is_done)\n",
        "\n",
        "# Note: as you can see, the car has moved to the right slightly (around 0.0005)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PrD9mcOmpr6f"
      },
      "source": [
        "### Play with it\n",
        "\n",
        "Below is the code that drives the car to the right. However, if you simply use the default policy, the car will not reach the flag at the far right due to gravity.\n",
        "\n",
        "__Your task__ is to fix it. Find a strategy that reaches the flag. \n",
        "\n",
        "You are not required to build any sophisticated algorithms for now, and you definitely don't need to know any reinforcement learning for this. Feel free to hard-code :)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4qv_3SBOpr6g"
      },
      "outputs": [],
      "source": [
        "from IPython import display\n",
        "\n",
        "# Create env manually to set time limit. Please don't change this.\n",
        "TIME_LIMIT = 250\n",
        "env = gym.wrappers.TimeLimit(\n",
        "    gym.envs.classic_control.MountainCarEnv(),\n",
        "    max_episode_steps=TIME_LIMIT + 1,\n",
        ")\n",
        "actions = {'left': 0, 'stop': 1, 'right': 2}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-eYqGpxBpr6g"
      },
      "outputs": [],
      "source": [
        "actions = {'left': 0, 'stop': 1, 'right': 2}\n",
        "def policy(obs, t):\n",
        "    # Write the code for your policy here. You can use the observation\n",
        "    # (a tuple of position and velocity), the current time step, or both,\n",
        "    # if you want.\n",
        "    position, velocity = obs\n",
        "    if velocity<0:\n",
        "      return actions['left']\n",
        "    else:\n",
        "      return actions['right']  \n",
        "\n",
        "    # This is an example policy. You can try running it, but it will not work.\n",
        "    # Your goal is to fix that. You don't need anything sophisticated here,\n",
        "    # and you can hard-code any policy that seems to work.\n",
        "    # Hint: think how you would make a swing go farther and faster.\n",
        "    #return actions['right']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 201
        },
        "id": "NJv8DYh3pr6h",
        "outputId": "2b89040c-255a-45db-ecd2-26f41bf17ae2"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(4, 3))\n",
        "display.clear_output(wait=True)\n",
        "\n",
        "obs = env.reset()\n",
        "for t in range(TIME_LIMIT):\n",
        "    plt.gca().clear()\n",
        "    \n",
        "    action = policy(obs, t)  # Call your policy\n",
        "    obs, reward, done, _ = env.step(action)  # Pass the action chosen by the policy to the environment\n",
        "    \n",
        "    # We don't do anything with reward here because MountainCar is a very simple environment,\n",
        "    # and reward is a constant -1. Therefore, your goal is to end the episode as quickly as possible.\n",
        "\n",
        "    # Draw game image on display.\n",
        "    plt.imshow(env.render('rgb_array'))\n",
        "    plt.savefig('/content/drive/MyDrive/RL_proj_car_images/car_img_iter'+str(t)+'.png')\n",
        "    display.display(plt.gcf())\n",
        "    display.clear_output(wait=True)\n",
        "\n",
        "    if done:\n",
        "        print(\"Well done!\")\n",
        "        break\n",
        "else:\n",
        "    print(\"Time limit exceeded. Try again.\")\n",
        "\n",
        "display.clear_output(wait=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e4ZrUrCXDO1w",
        "outputId": "aa9cf624-b0fb-4851-a374-08c91dbf0e65"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "It took step 122\n"
          ]
        }
      ],
      "source": [
        "print('It took step', t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NCpldGrMDd3q",
        "outputId": "e60e9be6-df4e-4f82-e611-6d3c1aeee940"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LTDfJTLRpr6n"
      },
      "outputs": [],
      "source": [
        "assert obs[0] > 0.47\n",
        "print(\"You solved it!\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wSscSOQbOKXU"
      },
      "source": [
        "Try random policy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gPR8FQ65On9D",
        "outputId": "470c3c6d-84d3-4b30-8efb-9c1b2cb57547"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.random.choice([0,1,2])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 201
        },
        "id": "0avlf4GoOMnL",
        "outputId": "e4d0f4d6-6267-4f7c-cfb0-521bf431bd59"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 288x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def rand_policy(obs, t):\n",
        "    return np.random.choice([0,1,2])\n",
        "TIME_LIMIT=500\n",
        "plt.figure(figsize=(4, 3))\n",
        "display.clear_output(wait=True)\n",
        "\n",
        "obs = env.reset()\n",
        "for t in range(TIME_LIMIT):\n",
        "    plt.gca().clear()\n",
        "    \n",
        "    action = rand_policy(obs, t)  # Call your policy\n",
        "    obs, reward, done, _ = env.step(action)  # Pass the action chosen by the policy to the environment\n",
        "    \n",
        "    # We don't do anything with reward here because MountainCar is a very simple environment,\n",
        "    # and reward is a constant -1. Therefore, your goal is to end the episode as quickly as possible.\n",
        "\n",
        "    # Draw game image on display.\n",
        "    plt.imshow(env.render('rgb_array'))\n",
        "    #plt.savefig('/content/drive/MyDrive/RL_proj_car_images/car_img_iter'+str(t)+'.png')\n",
        "    display.display(plt.gcf())\n",
        "    display.clear_output(wait=True)\n",
        "\n",
        "    if done:\n",
        "        print(\"Well done!\")\n",
        "        break\n",
        "else:\n",
        "    print(\"Time limit exceeded. Try again.\")\n",
        "\n",
        "display.clear_output(wait=True)"
      ]
    }
  ],
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