Q_learning_CartPole.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "RL_assignment2.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNnhjWxF7KjjWT608Ri6TSH",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/harmanpreet93/reinforcement-learning-COMP-767/blob/master/Q_learning_CartPole.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qcp3ODpuvIQS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a7e4efc6-a327-499b-8f84-370759bbfa5b"
      },
      "source": [
        "import gym\n",
        "import random\n",
        "from tqdm import tqdm\n",
        "import matplotlib.pyplot as plt\n",
        "from torch.autograd import Variable\n",
        "from IPython.display import clear_output\n",
        "\n",
        "# ! pip install tensorflow==2.1.0\n",
        "import tensorflow as tf\n",
        "tf.__version__"
      ],
      "execution_count": 162,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'2.1.0'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 162
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KeMS7kPmlVVk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_res(values, title=''):   \n",
        "    ''' Plot the reward curve and histogram of results over time.'''\n",
        "    # Update the window after each episode\n",
        "    clear_output(wait=True)\n",
        "    \n",
        "    # Define the figure\n",
        "    f, ax = plt.subplots(nrows=1, ncols=2, figsize=(12,5))\n",
        "    f.suptitle(title)\n",
        "    ax[0].plot(values, label='score per run')\n",
        "    ax[0].axhline(195, c='red',ls='--', label='goal')\n",
        "    ax[0].set_xlabel('Episodes')\n",
        "    ax[0].set_ylabel('Reward')\n",
        "    x = range(len(values))\n",
        "    ax[0].legend()\n",
        "    # Calculate the trend\n",
        "    try:\n",
        "        z = np.polyfit(x, values, 1)\n",
        "        p = np.poly1d(z)\n",
        "        ax[0].plot(x,p(x),\"--\", label='trend')\n",
        "    except:\n",
        "        print('')\n",
        "    \n",
        "    # Plot the histogram of results\n",
        "    ax[1].hist(values[-50:])\n",
        "    ax[1].axvline(195, c='red', label='goal')\n",
        "    ax[1].set_xlabel('Scores per Last 50 Episodes')\n",
        "    ax[1].set_ylabel('Frequency')\n",
        "    ax[1].legend()\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9AA9YcPTCKIP",
        "colab_type": "code",
        "outputId": "565bee2e-cf8e-437d-c3e6-250e66c03546",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "env = gym.make('CartPole-v1')\n",
        "env.reset()\n",
        "\n",
        "discount_rate = 0.9\n",
        "epsilon = 0.1\n",
        "step_size = 0.1 # learning rate\n",
        "n_obs_space = len(env.observation_space.high)\n",
        "n_actions = env.action_space.n\n",
        "\n",
        "n_hidden = 64\n",
        "\n",
        "class Model(tf.keras.Model):\n",
        "\n",
        "    def __init__(self, n_states, n_actions, hidden_dim=64, lr=0.05):\n",
        "        super(Model, self).__init__()\n",
        "        self.dense1 = tf.keras.layers.Dense(n_hidden, input_shape=(n_states,), activation='relu')\n",
        "        self.dense2 = tf.keras.layers.Dense(n_hidden, activation='relu')\n",
        "        self.logits = tf.keras.layers.Dense(n_actions)\n",
        "\n",
        "    def call(self, inputs):\n",
        "        x = self.dense1(inputs)\n",
        "        x = self.dense2(x)\n",
        "        return self.logits(x)\n",
        "\n",
        "\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=0.05)\n",
        "loss_fn = tf.keras.losses.MeanSquaredError()\n",
        "train_loss = tf.keras.metrics.MeanSquaredError()\n",
        "train_accuracy = tf.keras.metrics.Accuracy()\n",
        "\n",
        "@tf.function\n",
        "def train_step(inputs, y_true, optimizer, loss_fn):\n",
        "    with tf.GradientTape() as tape:\n",
        "        # training=True is only needed if there are layers with different\n",
        "        # behavior during training versus inference (e.g. Dropout).\n",
        "        y_pred = model(inputs, training=True)\n",
        "        loss = loss_fn(y_true, y_pred)\n",
        "    gradients = tape.gradient(loss, model.trainable_variables)\n",
        "    optimizer.apply_gradients(zip(gradients, model.trainable_variables))\n",
        "\n",
        "    return y_pred, y_true, loss"
      ],
      "execution_count": 268,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/gym/logger.py:30: UserWarning: \u001b[33mWARN: Box bound precision lowered by casting to float32\u001b[0m\n",
            "  warnings.warn(colorize('%s: %s'%('WARN', msg % args), 'yellow'))\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eIdzkpa2njVD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JBWLnWwWTwpc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def replay(model, memory, buffer_size, discount_rate, optimizer, loss_fn):\n",
        "    if len(memory) > buffer_size:\n",
        "        X,y = [], []\n",
        "        # sample batch from memory\n",
        "        memory_batch = random.sample(memory, buffer_size)\n",
        "        for current_state, action, next_state, reward, done in memory_batch:\n",
        "            X.append(current_state)\n",
        "            input_vector = np.reshape(current_state, (1,*current_state.shape))\n",
        "            q_values = model(input_vector).numpy()[0]\n",
        "            if done:\n",
        "                q_values[action] = reward\n",
        "            else:\n",
        "                input_vector = np.reshape(next_state, (1,*next_state.shape))\n",
        "                q_values_next = model(input_vector)\n",
        "                print(q_values_next)\n",
        "                q_values[action] = reward + discount_rate * np.max(q_values_next)\n",
        "            y.append(q_values)\n",
        "\n",
        "        X = np.array(X)\n",
        "        y = np.array(y)\n",
        "        dataset = tf.data.Dataset.from_tensor_slices((X,y)).batch(1)\n",
        "        \n",
        "        # train model here\n",
        "        train_step(X, y, optimizer, loss_fn)\n",
        "\n",
        "        n_epochs = 10\n",
        "        for epoch in range(n_epochs):\n",
        "\n",
        "            for minibatch in dataset:\n",
        "                train_step(minibatch[0], minibatch[-1], optimizer, loss_fn)\n",
        "\n",
        "                train_loss(loss)\n",
        "                train_accuracy(y_true, y_pred)\n",
        "\n",
        "                template = 'Episode {}, Loss: {}, Accuracy: {}'\n",
        "                print(template.format(episode+1,\n",
        "                                train_loss.result(),\n",
        "                                train_accuracy.result()*100))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RP0EEzx3wL7x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "outputId": "541a42cc-2d5b-4e68-e26b-ec42726d5d40"
      },
      "source": [
        "model = Model(n_obs_space, n_actions, hidden_dim=64)\n",
        "\n",
        "n_episodes = 100\n",
        "replay_buffer_size = 20\n",
        "memory = []\n",
        "reward_list = []\n",
        "memory_index = 0\n",
        "\n",
        "for episode in range(n_episodes):\n",
        "    train_loss.reset_states()\n",
        "    train_accuracy.reset_states()\n",
        "\n",
        "    done = False\n",
        "    current_state = env.reset()\n",
        "    total_reward = 0\n",
        "    memory = []\n",
        "\n",
        "    while not done:\n",
        "        # choose action based on epsilon-greedy policy\n",
        "        if np.random.random() < epsilon:\n",
        "            action = env.action_space.sample()\n",
        "        else:\n",
        "            input_vector = np.reshape(state, (1,*state.shape))\n",
        "            Q_output = model(input_vector)\n",
        "            action = np.argmax(Q_output)\n",
        "\n",
        "        # take chosen action\n",
        "        next_state, reward, done, info = env.step(action)\n",
        "        # add reward\n",
        "        total_reward += reward\n",
        "\n",
        "        # save states and action in memory\n",
        "        memory.append((current_state, action, next_state, reward, done))\n",
        "\n",
        "        if done:\n",
        "            break\n",
        "        \n",
        "        replay(model, memory, replay_buffer_size, discount_rate, optimizer, loss_fn)\n",
        "        current_state = next_state\n",
        "\n",
        "    reward_list.append(total_reward)\n",
        "    plot_res(reward_list)"
      ],
      "execution_count": 276,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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s+CovvleHeUVEJLEMBQYAg4FLgwK5rh4E+gCDgGzgvpomdPdJ7p7p7pnp6en1ySsi0mDU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\nFtdBEARBEARBUCL+Br+KQd0+czlIAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vIWmc4SJkqyR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "plot_res(reward_list)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X153Nolp3GHy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "d9ef3fdf-5daf-4a76-8d74-e2c02b16d865"
      },
      "source": [
        "y[0], model(np.reshape(X[0], (1,*X[0].shape)))"
      ],
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([5.2412195, 6.847495 ], dtype=float32),\n",
              " <tf.Tensor: shape=(1, 2), dtype=float32, numpy=array([[5.250276, 6.652201]], dtype=float32)>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 170
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PUhMJgT60C1D",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "4727624b-75b7-4ace-8998-965a88ae64c6"
      },
      "source": [
        "print(train_X.shape, train_y.shape)"
      ],
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(98, 4) (98, 2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6BhdaXXHisuG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YLPH-pwrwMWM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class DQN():\n",
        "    ''' Deep Q Neural Network class. '''\n",
        "    def __init__(self, state_dim, action_dim, hidden_dim=64, lr=0.05):\n",
        "            self.criterion = torch.nn.MSELoss()\n",
        "            self.model = torch.nn.Sequential(\n",
        "                            torch.nn.Linear(state_dim, hidden_dim),\n",
        "                            torch.nn.LeakyReLU(),\n",
        "                            torch.nn.Linear(hidden_dim, hidden_dim*2),\n",
        "                            torch.nn.LeakyReLU(),\n",
        "                            torch.nn.Linear(hidden_dim*2, action_dim)\n",
        "                    )\n",
        "            self.optimizer = torch.optim.Adam(self.model.parameters(), lr)\n",
        "\n",
        "    def update(self, state, y):\n",
        "            \"\"\"Update the weights of the network given a training sample. \"\"\"\n",
        "            y_pred = self.model(torch.Tensor(state))\n",
        "            loss = self.criterion(y_pred, Variable(torch.Tensor(y)))\n",
        "            self.optimizer.zero_grad()\n",
        "            loss.backward()\n",
        "            self.optimizer.step()\n",
        "            \n",
        "    def predict(self, state):\n",
        "            \"\"\" Compute Q values for all actions using the DQL. \"\"\"\n",
        "            with torch.no_grad():\n",
        "                return self.model(torch.Tensor(state))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OO2hgWV85dsK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def q_learning(env, model, episodes, gamma=0.9, \n",
        "               epsilon=0.3, eps_decay=0.99,\n",
        "               replay=False, replay_size=20, \n",
        "               title = 'DQL', double=False, \n",
        "               n_update=10, soft=False):\n",
        "    \"\"\"Deep Q Learning algorithm using the DQN. \"\"\"\n",
        "    final = []\n",
        "    memory = []\n",
        "    for episode in range(episodes):\n",
        "        # Reset state\n",
        "        state = env.reset()\n",
        "        done = False\n",
        "        total = 0\n",
        "        \n",
        "        while not done:\n",
        "            # Implement greedy search policy to explore the state space\n",
        "            if random.random() < epsilon:\n",
        "                action = env.action_space.sample()\n",
        "            else:\n",
        "                q_values = model.predict(state)\n",
        "                action = torch.argmax(q_values).item()\n",
        "            \n",
        "            # Take action and add reward to total\n",
        "            next_state, reward, done, _ = env.step(action)\n",
        "            \n",
        "            # Update total and memory\n",
        "            total += reward\n",
        "            memory.append((state, action, next_state, reward, done))\n",
        "            q_values = model.predict(state).tolist()\n",
        "             \n",
        "            if done:\n",
        "                break\n",
        "\n",
        "            # Update network weights using replay memory\n",
        "            model.replay(memory, replay_size, gamma)\n",
        "            state = next_state\n",
        "        \n",
        "        # Update epsilon\n",
        "        epsilon = max(epsilon * eps_decay, 0.01)\n",
        "        final.append(total)\n",
        "        plot_res(final, title)\n",
        "    return final"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KyMPy_X4M737",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Expand DQL class with a replay function.\n",
        "class DQN_replay(DQN):\n",
        "    def replay(self, memory, size, gamma=0.9):\n",
        "        \"\"\" Add experience replay to the DQN network class. \"\"\"\n",
        "        # Make sure the memory is big enough\n",
        "        if len(memory) >= size:\n",
        "            states = []\n",
        "            targets = []\n",
        "            # Sample a batch of experiences from the agent's memory\n",
        "            batch = random.sample(memory, size)\n",
        "            \n",
        "            # Extract information from the data\n",
        "            for state, action, next_state, reward, done in batch:\n",
        "                states.append(state)\n",
        "                # Predict q_values\n",
        "                q_values = self.predict(state).tolist()\n",
        "                if done:\n",
        "                    q_values[action] = reward\n",
        "                else:\n",
        "                    q_values_next = self.predict(next_state)\n",
        "                    q_values[action] = reward + gamma * torch.max(q_values_next).item()\n",
        "\n",
        "                targets.append(q_values)\n",
        "\n",
        "            self.update(states, targets)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z1FmwShVjih-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "outputId": "cd92e122-c3db-4f49-9b36-937c82347350"
      },
      "source": [
        "# Get replay results\n",
        "dqn_replay = DQN_replay(n_obs_space, n_actions, n_hidden, lr=0.05)\n",
        "\n",
        "replay = q_learning(env, dqn_replay, \n",
        "                    episodes=150, gamma=.9, \n",
        "                    epsilon=0.2, replay=True, \n",
        "                    title='DQL with Replay')"
      ],
      "execution_count": 281,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BbwOfdfeeaKO7v2xmlzRuWCIi6aRgeppSZjrd3J1sJly0RWUeMrneDfS4ewnA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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GD5JJsLJaC4q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}