Q-Learning_lessons.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Q-Learning\n",
    "<hr>\n",
    "Author: Sahil Johari (http://www.sahiljohari.com/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, I am going to try creating Q-learning models from simple to complex levels to solve certain standard problems pre-existing on https://gym.openai.com\n",
    "\n",
    "Let's get started!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Level 1: A simple model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reinforcement learning, explained simply, is a computational approach where an agent interacts with an environment by taking actions in which it tries to maximize an accumulated reward. Here is a simple graph, which I will be referring to often:"
   ]
  },
  {
   "attachments": {
    "Q_learning.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Q_learning.PNG](attachment:Q_learning.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An agent in a current state (St) takes an action (At) to which the environment reacts and responds, returning a new state(St+1) and reward (Rt+1) to the agent. Given the updated state and reward, the agent chooses the next action, and the loop repeats until an environment is solved or terminated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym\n",
    "from gym import envs\n",
    "\n",
    "import numpy as np\n",
    "import time\n",
    "from IPython.display import display, clear_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "env = gym.make('Taxi-v2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "254"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The starting state which is random\n",
    "env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gives all the possible states in this environment\n",
    "env.observation_space.n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : : : : |\n",
      "| : :\u001b[43m \u001b[0m: : |\n",
      "| | : | : |\n",
      "|\u001b[35mY\u001b[0m| : |\u001b[34;1mB\u001b[0m: |\n",
      "+---------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "env.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gives the number of actions available to our agent\n",
    "env.action_space.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The six possible actions are: down (0), up (1), right (2), left (3), pick-up (4), and drop-off (5)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "|\u001b[43m \u001b[0m: : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|\u001b[35mY\u001b[0m| : |\u001b[34;1mB\u001b[0m: |\n",
      "+---------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Overriding the current state to 114 for learning purpose\n",
    "env.env.s = 114\n",
    "env.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|\u001b[43mR\u001b[0m: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|\u001b[35mY\u001b[0m| : |\u001b[34;1mB\u001b[0m: |\n",
      "+---------+\n",
      "  (North)\n"
     ]
    }
   ],
   "source": [
    "env.step(1)\n",
    "env.render()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we moved 'up' by taking step (1) which corresponds to \"up\" action."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(14, -1, False, {'prob': 1.0})\n"
     ]
    }
   ],
   "source": [
    "print(env.step(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These values are (state, reward, done, info)\n",
    "\n",
    "Now that we have explored the basics, let's start again with a fresh code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6013\n"
     ]
    }
   ],
   "source": [
    "state = env.reset()\n",
    "counter = 0\n",
    "reward = None\n",
    "\n",
    "while reward != 20:\n",
    "    state, reward, done, info = env.step(env.action_space.sample())\n",
    "    counter += 1\n",
    "\n",
    "print(counter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above code, we saw that it took 1870 steps for our agent to reach the goal (or achieve a reward of 20, which is the goal). This approach is a _random policy approach_ in which the agent is trying out random actions until it gets the maximum reward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to have the algorithm remember its actions and their associated rewards. In this case, the algorithm’s memory is going to be a *Q action value table*.\n",
    "\n",
    "To manage this Q table, we will use a NumPy array. The size of this table will be the number of states (500) by the number of possible actions (6)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = np.zeros([env.observation_space.n, env.action_space.n])"
   ]
  },
  {
   "attachments": {
    "Bellman_equation.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Bellman_equation.PNG](attachment:Bellman_equation.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Over multiple episodes of trying to solve the problem, we will be updating our Q values using the Bellman equation shown above, slowly improving our algorithm’s efficiency and performance. We will also want to track our total accumulated reward for each episode, which we will define as **G**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = 0\n",
    "alpha = 0.618 #learning rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 7900 State: 479 Total Reward: 33080\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "None"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|Y| : |\u001b[35m\u001b[42mB\u001b[0m\u001b[0m: |\n",
      "+---------+\n",
      "  (Dropoff)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "None"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, a very basic Q-learning algorithm\n",
    "\n",
    "for episode in range(8000):\n",
    "    done = False\n",
    "    reward = 0\n",
    "    state = env.reset()\n",
    "    \n",
    "    while not done:\n",
    "        action = np.argmax(Q[state]) #1\n",
    "        state1, reward, done, info = env.step(action) #2\n",
    "        Q[state,action] += alpha * (reward + np.max(Q[state1]) - Q[state,action]) #3\n",
    "        G += reward\n",
    "        state = state1\n",
    "    if episode % 100 == 0:\n",
    "        display(print('Episode {} State: {} Total Reward: {}'.format(episode,state, G)))\n",
    "        display(env.render())\n",
    "        time.sleep(0.1)\n",
    "        clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-First (#1): The agent starts by choosing an action with the highest Q value for the current state using argmax. Argmax will return the index/action with the highest value for that state. Initially, our Q table will be all zeros. But, after every step, the Q values for state-action pairs will be updated.\n",
    "\n",
    "-Second (#2): The agent then takes action and we store the future state as state2 (St+1). This will allow the agent to compare the previous state to the new state.\n",
    "\n",
    "-Third (#3): We update the state-action pair (St , At) for Q using the reward, and the max Q value for state2 (St+1). This update is done using the action value formula (based upon the Bellman equation) and allows state-action pairs to be updated in a recursive fashion (based on future values). Note that we still do not have a discount factor included in this model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "# Level 2: Life is all about Balance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this level, I am going to try out a new environment from the Gym toolkit called _CartPole_."
   ]
  },
  {
   "attachments": {
    "cartpole.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![cartpole.PNG](attachment:cartpole.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea is to teach our agent to balance a pole placed on a cart. Let's dive into it and see if I can create an agent based on what I've learnt before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Things I need to write the code:\n",
    "* Q-table\n",
    "* learning rate\n",
    "* discount factor\n",
    "* reward\n",
    "* action\n",
    "* state\n",
    "* epsilon\n",
    "* observation time-step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\sahil\\Anaconda3\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Code adapted from: https://github.com/llSourcell/deep_q_learning/blob/master/03_PlayingAgent.ipynb\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython import display\n",
    "\n",
    "from sklearn import metrics as mt\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Flatten, Dropout\n",
    "from keras.optimizers import Adam, Adagrad\n",
    "from collections import deque            # For storing moves \n",
    "\n",
    "import numpy as np\n",
    "import gym\n",
    "\n",
    "import random     # For sampling batches from the observations\n",
    "import timeit\n",
    "\n",
    "import warnings\n",
    "warnings.simplefilter(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARN: gym.spaces.Box autodetected dtype as <class 'numpy.float32'>. Please provide explicit dtype.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "env_name = 'CartPole-v1'\n",
    "env = gym.make(env_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Helper function to render output using matplotlib\n",
    "def show_state(env, episode, step=0, info=\"\"):\n",
    "    plt.figure(3)\n",
    "    plt.clf()\n",
    "    plt.imshow(env.render(mode='rgb_array'))\n",
    "    plt.title(\"%s Episode: %d | Step: %d %s\" % (env.spec.id, episode, step, info))\n",
    "    plt.axis('off')\n",
    "    \n",
    "    display.display(plt.gcf())\n",
    "    display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 2, 200)            1000      \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 2, 200)            0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 400)               0         \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 50)                20050     \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 50)                0         \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 10)                510       \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 2)                 22        \n",
      "=================================================================\n",
      "Total params: 21,582\n",
      "Trainable params: 21,582\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "# Create network. Input is two consecutive game states, output is Q-values of the possible moves.\n",
    "model = Sequential()\n",
    "model.add(Dense(200, input_shape=(2,) + env.observation_space.shape, activation='relu'))\n",
    "model.add(Dropout(0.8))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(50, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(10, activation='relu'))\n",
    "model.add(Dense(env.action_space.n, activation='softmax'))\n",
    "model.compile(loss='mse', optimizer='adam', metrics=['accuracy'])\n",
    "\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A reinforcement learning problem is characterized by the following components:\n",
    "\n",
    "* A state space, which is the set of all possible states,\n",
    "* An action space, which is the set of all possible actions,\n",
    "* A cost function, which measures how bad a state is,\n",
    "* A time horizon, which is the number of time steps,\n",
    "* An initial state probability distribution, which specifies how frequently different states occur at the beginning before any action is taken, and\n",
    "* A state transition probability distribution, which specifies how the state changes (probabilistically) after a particular action is taken."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define parameters\n",
    "learning_rate = 0.01\n",
    "gamma = 0.9\n",
    "eps = 0.4\n",
    "time_steps = 5000\n",
    "mb_size = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total time-steps to observe: 5000\n",
      "Observation Truely complete in 5000 time-steps\n"
     ]
    }
   ],
   "source": [
    "# Observe: Discover what each action does\n",
    "done = False\n",
    "\n",
    "# forcing the agent to achieve the goal while exploring\n",
    "while not done:\n",
    "    action_list = deque()\n",
    "    observation = env.reset()\n",
    "    obs = np.expand_dims(observation, axis=0)\n",
    "    state = np.stack((obs, obs) , axis=1)\n",
    "    \n",
    "    for _ in range(time_steps):\n",
    "        # pick a random action if we are below the epsilon value\n",
    "        if np.random.rand() <= eps:\n",
    "            action = np.random.randint(0, env.action_space.n)\n",
    "        else:\n",
    "            Q = model.predict(state)\n",
    "            action = np.argmax(Q)\n",
    "\n",
    "        observation_new, reward, done, info = env.step(action)\n",
    "        obs_new = np.expand_dims(observation_new, axis=0)\n",
    "        state_new = np.append(np.expand_dims(obs_new, axis=0), state[:, :1, :], axis=1)\n",
    "\n",
    "        # This is like training data being generated by observing the environment\n",
    "        action_list.append((state, action, reward, state_new, done))\n",
    "        state = state_new\n",
    "\n",
    "        if done:\n",
    "            env.reset()\n",
    "            obs = np.expand_dims(observation, axis=0)\n",
    "            state = np.stack((obs, obs) , axis=1)\n",
    "\n",
    "print('Total time-steps to observe: {}'.format(time_steps))\n",
    "print('Observation {}ly complete in {} time-steps'.format(done, len(action_list)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete!\n"
     ]
    }
   ],
   "source": [
    "# Train: Use the observations from before and train the agent\n",
    "model_history = []\n",
    "# Sample some moves\n",
    "minibatch = random.sample(action_list, mb_size)                             \n",
    "\n",
    "# Prepare input (X_train) and target (y_train) variables\n",
    "X_train = np.zeros((mb_size,)+state.shape[1:])\n",
    "y_train = np.zeros((mb_size, env.action_space.n))\n",
    "\n",
    "for i in range(mb_size):\n",
    "    [_state, _action, _reward, _state_new, _done] = [minibatch[i][j] for j in range(0, 5)]\n",
    "    \n",
    "    # Build Bellman equation for Q-function\n",
    "    X_train[i:i+1] = np.expand_dims(_state, axis=0)\n",
    "    y_train[i] = model.predict(_state)\n",
    "    Q_train = model.predict(_state_new)\n",
    "    \n",
    "    if _done:\n",
    "        y_train[i, _action] = _reward\n",
    "    else:\n",
    "        y_train[i, _action] = _reward + gamma * np.max(Q_train)\n",
    "    \n",
    "    hist = model.fit(X_train, y_train, epochs=1, verbose=0)\n",
    "    model_history.append(hist.history['acc'])\n",
    "#     model.train_on_batch(X_train, y_train)\n",
    "    \n",
    "print('Training complete!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2198c6ed160>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(model_history, label=\"Training Accuracy\")\n",
    "plt.xlabel('Batch')\n",
    "plt.ylabel('Accuracy %')\n",
    "plt.title('Model Accuracy per Batch')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Game ended! Total reward: 10.0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run: Play the environment to see how well it is doing based on the training above\n",
    "episodes = 50 # should run for more episodes than this\n",
    "time_per_episode=[]\n",
    "for episode in range(1, episodes+1):\n",
    "    observation = env.reset()\n",
    "    obs = np.expand_dims(observation, axis=0)\n",
    "    state = np.stack((obs, obs) , axis=1)\n",
    "    done = False\n",
    "    reward_total = 0.0\n",
    "    action = 0\n",
    "    info = None\n",
    "    start = timeit.default_timer()\n",
    "    while not done:\n",
    "        show_state(env, episode, step=action)\n",
    "        Q = model.predict(state)\n",
    "        action = np.argmax(Q)\n",
    "        observation, reward, done, info = env.step(action)\n",
    "        obs = np.expand_dims(observation, axis=0)\n",
    "        state = np.append(np.expand_dims(obs, axis=0), state[:, :1, :], axis=1)    \n",
    "        reward_total += reward\n",
    "    time_per_episode.append(timeit.default_timer() - start)\n",
    "\n",
    "    \n",
    "print('Game ended! Total reward: {}'.format(reward_total))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21996eee9e8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time_per_episode, label=\"Time\")\n",
    "plt.xlabel('Episode')\n",
    "plt.ylabel('Time in milliseconds')\n",
    "plt.title('Time spent per episode')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.save_weights('basic_dqn_{}_weights.h5f'.format(env_name), overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, it seems to work. Probably training for more episodes might make the agent achieve its goal. So far, this model is good to work with environments which have _discrete_ action space.\n",
    "\n",
    "Next, I am going to dig a little more on the implementation of various kinds of models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "# Level 3: Using Keras-RL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am going to use the Keras-rl library which has got implementations for reinforcement learning methods, one of which I implemented (Q-learning) in the previous level. This is to understand and explore more about what's going on under the hood.\n",
    "\n",
    "Let's get started!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\sahil\\Anaconda3\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Code adapted from: https://github.com/keras-rl/keras-rl/blob/master/examples/dqn_cartpole.py\n",
    "import numpy as np\n",
    "import gym\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation, Flatten\n",
    "from keras.optimizers import Adam\n",
    "\n",
    "from rl.agents.dqn import DQNAgent\n",
    "from rl.policy import BoltzmannQPolicy\n",
    "from rl.memory import SequentialMemory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "envs = ['Acrobot-v1', 'CartPole-v1', 'MountainCar-v0']\n",
    "env_num = 2\n",
    "if not env_num > 3 and not env_num < 0:\n",
    "    ENV_NAME = envs[env_num]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARN: gym.spaces.Box autodetected dtype as <class 'numpy.float32'>. Please provide explicit dtype.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# Setup the environment\n",
    "env = gym.make(ENV_NAME)\n",
    "np.random.seed(0)\n",
    "env.seed(0)\n",
    "\n",
    "num_actions = env.action_space.n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten_1 (Flatten)          (None, 2)                 0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 16)                48        \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 16)                272       \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 16)                272       \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 3)                 51        \n",
      "=================================================================\n",
      "Total params: 643\n",
      "Trainable params: 643\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "# Build a model\n",
    "model = Sequential()\n",
    "model.add(Flatten(input_shape=(1,)+env.observation_space.shape))\n",
    "model.add(Dense(16, activation='relu'))\n",
    "model.add(Dense(16, activation='relu'))\n",
    "model.add(Dense(16, activation='relu'))\n",
    "model.add(Dense(num_actions, activation='softmax'))\n",
    "\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important to know the different kinds of _Agent_ implementations. Here's a summary:\n",
    "\n",
    "|Name|Action Space|\n",
    "|----|------------|\n",
    "|DQN |discrete|\n",
    "|DDPG|continuous|\n",
    "|NAF |continuous|\n",
    "|CEM |discrete|\n",
    "|SARSA|discrete|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For reference, I am going to list down all the policy implementations that Keras-RL provides:\n",
    "* **LinearAnnealedPolicy**: computes a current threshold value and transfers it to an inner policy which chooses the action. The threshold value is following a linear function decreasing over time.\n",
    "* **EpsGreedyQPolicy**: either takes a random action with probability epsilon or takes current best action with prob (1 - epsilon).\n",
    "* **GreedyQPolicy**: returns the current best action according to q_values.\n",
    "* **BoltzmannQPolicy**: builds a probability law on q values and returns an action selected randomly according to this law.\n",
    "* **MaxBoltzmannQPolicy**: combination of the eps-greedy and Boltzman q-policy.\n",
    "* **BoltzmannGumbelQPolicy**: Implements Boltzmann-Gumbel exploration (BGE) adapted for Q learning based on the paper Boltzmann Exploration Done Right (https://arxiv.org/pdf/1705.10257.pdf). BGE is invariant with respect to the mean of the rewards but not their variance. The parameter C, which defaults to 1, can be used to correct for this, and should be set to the least upper bound on the standard deviation of the rewards. BGE is only available for training, not testing. For testing purposes, you can achieve approximately the same result as BGE after training for N steps on K actions with parameter C by using the BoltzmannQPolicy and setting tau = C/sqrt(N/K)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure and compile our agent\n",
    "memory = SequentialMemory(limit=50000, window_length=1)\n",
    "policy = BoltzmannQPolicy()\n",
    "dqn = DQNAgent(model=model, nb_actions = num_actions, memory=memory, nb_steps_warmup = 15, \n",
    "               target_model_update=1e-2, policy=policy)\n",
    "dqn.compile(Adam(lr=1e-3), metrics=['mae', 'accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training for 20000 steps ...\n",
      "Interval 1 (0 steps performed)\n",
      "10000/10000 [==============================] - 60s 6ms/step - reward: -1.0000\n",
      "50 episodes - episode_reward: -200.000 [-200.000, -200.000] - loss: 0.492 - mean_absolute_error: 0.553 - acc: 0.467 - mean_q: 0.349\n",
      "\n",
      "Interval 2 (10000 steps performed)\n",
      "10000/10000 [==============================] - 59s 6ms/step - reward: -1.0000\n",
      "done, took 119.679 seconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x20c1e7e6940>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Time to learn something\n",
    "dqn.fit(env, nb_steps=20000, visualize=False, verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the final weights after training\n",
    "dqn.save_weights('dqn_{}_weights.h5f'.format(ENV_NAME), overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing for 20 episodes ...\n",
      "Episode 1: reward: -200.000, steps: 200\n",
      "Episode 2: reward: -200.000, steps: 200\n",
      "Episode 3: reward: -200.000, steps: 200\n",
      "Episode 4: reward: -200.000, steps: 200\n",
      "Episode 5: reward: -200.000, steps: 200\n",
      "Episode 6: reward: -200.000, steps: 200\n",
      "Episode 7: reward: -200.000, steps: 200\n",
      "Episode 8: reward: -200.000, steps: 200\n",
      "Episode 9: reward: -200.000, steps: 200\n",
      "Episode 10: reward: -200.000, steps: 200\n",
      "Episode 11: reward: -200.000, steps: 200\n",
      "Episode 12: reward: -200.000, steps: 200\n",
      "Episode 13: reward: -200.000, steps: 200\n",
      "Episode 14: reward: -200.000, steps: 200\n",
      "Episode 15: reward: -200.000, steps: 200\n",
      "Episode 16: reward: -200.000, steps: 200\n",
      "Episode 17: reward: -200.000, steps: 200\n",
      "Episode 18: reward: -200.000, steps: 200\n",
      "Episode 19: reward: -200.000, steps: 200\n",
      "Episode 20: reward: -200.000, steps: 200\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x20c20028f60>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test the algorithm for 20 episodes\n",
    "dqn.test(env, nb_episodes=20, visualize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, I explored the concept of _Reinforcement Learning_ by learning and implementing a basic Q-learning model on environments provided by Gym. I then moved on to creating a simple neural network to enhance the Q-function and apply it on a different environment, which delivered a decent performance. Further, I found a library called _Keral RL_ which consists of all the implementations of reinforcement learning and is easy to pull and build a model upon.\n",
    "\n",
    "In my future work, I am going to take up a few 2-D games and try out a model to train an agent for playing them.\n",
    "Do check out my website [here](http://www.sahiljohari.com/) and my work on Github (link on the website)."
   ]
  }
 ],
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