Reinforcement_CartPole.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Template for reinforcement learning applied to the CartPole benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/remy/.local/lib/python3.6/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"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import gym\n",
    "import numpy as np\n",
    "import bisect\n",
    "import math\n",
    "import os\n",
    "import random\n",
    "import tensorflow as tf\n",
    "\n",
    "from agents.random_agent import run_episode_random_agent\n",
    "from agents.human_crafted_agent import human_decision, run_episode_human_crafted_agent\n",
    "\n",
    "tf.logging.set_verbosity(tf.logging.WARN)  # Remove Info logs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete(2)\n",
      "[ 0.03718286 -0.04773799 -0.04078356 -0.03653672]\n",
      "500\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(env.action_space)  # 0 or 1\n",
    "\n",
    "obs = env.reset()\n",
    "print(obs)  # position, velocity, angle, angular_velocity\n",
    "print(env._max_episode_steps)\n",
    "\n",
    "observation_space_dimension = env.observation_space.shape[0]\n",
    "print(observation_space_dimension)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observing the values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_episodes = 1000\n",
    "positions = []\n",
    "velocities = []\n",
    "angles = []\n",
    "angular_velocities = []\n",
    "\n",
    "for episode in range(0, nb_episodes):\n",
    "    obs = env.reset()\n",
    "    done = False\n",
    "    final_score = 0\n",
    "\n",
    "    while not done:\n",
    "        action = env.action_space.sample()\n",
    "        obs, reward, done, info = env.step(action)\n",
    "        position, velocity, angle, angular_velocity = obs\n",
    "        positions.append(position)\n",
    "        velocities.append(velocity)\n",
    "        angles.append(angle)\n",
    "        angular_velocities.append(angular_velocity)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(positions, bins=100)\n",
    "plt.xlabel('position');\n",
    "plt.ylabel('Occurence');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(velocities, bins=100)\n",
    "plt.xlabel('velocity');\n",
    "plt.ylabel('Occurence');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(angles, bins=100)\n",
    "plt.xlabel('angle');\n",
    "plt.ylabel('Occurence');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(angular_velocities, bins=100)\n",
    "plt.xlabel('angular_velocity');\n",
    "plt.ylabel('Occurence');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Policy gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "nb_neurons_input = 4  # len(obs)\n",
    "nb_neurons_hidden_layer = 4\n",
    "nb_neurons_output = 1\n",
    "\n",
    "X = tf.placeholder(shape=[None, nb_neurons_input], dtype=tf.float32, name=\"X\")\n",
    "\n",
    "with tf.name_scope(\"dnn\"): \n",
    "    initializer_w = tf.contrib.layers.xavier_initializer()\n",
    "    initializer_b = tf.zeros_initializer() \n",
    "    hidden = tf.layers.dense(X, nb_neurons_hidden_layer, \\\n",
    "                             activation=tf.nn.elu, \\\n",
    "                             kernel_initializer=tf.contrib.layers.xavier_initializer(), \\\n",
    "                             name=\"hidden\")\n",
    "    output = tf.layers.dense(hidden, nb_neurons_output, \n",
    "                             activation=tf.nn.sigmoid,\n",
    "                             name=\"output\")  # proba of moving kart to left\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Playing an episode - before training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_episode_neural_network(show_renderer=False):    \n",
    "    with tf.Session() as sess:\n",
    "        init.run()\n",
    "        obs = env.reset()\n",
    "        obs_pretty = obs.reshape(1, nb_neurons_input)\n",
    "        done = False\n",
    "        final_score = 0\n",
    "        while not done:\n",
    "            if show_renderer:\n",
    "                env.render()\n",
    "            proba_move_to_left = output.eval(feed_dict={X: obs_pretty})        \n",
    "            if random.uniform(0, 1) < proba_move_to_left:\n",
    "                action = 0  # move to left\n",
    "            else:\n",
    "                action = 1       \n",
    "            obs, reward, done, info = env.step(action) \n",
    "            if done:\n",
    "                break\n",
    "            final_score += reward\n",
    "    env.reset()\n",
    "    env.close()\n",
    "    return final_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = []\n",
    "nb_episodes = 100\n",
    "\n",
    "for i in range(0, nb_episodes):\n",
    "    episode_score = run_episode_neural_network()\n",
    "    scores.append(episode_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.33\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(np.mean(scores))\n",
    "plt.plot(scores)\n",
    "plt.xlabel('episodes')\n",
    "plt.ylabel('rewards')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A2C policy gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}