week01_intro/deep_crossentropy_method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Deep Crossentropy method\n",
    "\n",
    "In this section we'll extend your CEM implementation with neural networks! You will train a multi-layer neural network to solve simple continuous state space games. __Please make sure you're done with tabular crossentropy method from the previous notebook.__\n",
    "\n",
    "![img](https://tip.duke.edu/independent_learning/greek/lesson/digging_deeper_final.jpg)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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/spring20/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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# if you see \"<classname> has no attribute .env\", remove .env or update gym\n",
    "env = gym.make(\"CartPole-v0\").env\n",
    "\n",
    "env.reset()\n",
    "n_actions = env.action_space.n\n",
    "state_dim = env.observation_space.shape[0]\n",
    "\n",
    "plt.imshow(env.render(\"rgb_array\"))\n",
    "print(\"state vector dim =\", state_dim)\n",
    "print(\"n_actions =\", n_actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network Policy\n",
    "\n",
    "For this assignment we'll utilize the simplified neural network implementation from __[Scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPClassifier.html)__. Here's what you'll need:\n",
    "\n",
    "* `agent.partial_fit(states, actions)` - make a single training pass over the data. Maximize the probabilitity of :actions: from :states:\n",
    "* `agent.predict_proba(states)` - predict probabilities of all actions, a matrix of shape __[len(states), n_actions]__\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "\n",
    "agent = MLPClassifier(\n",
    "    hidden_layer_sizes=(20, 20),\n",
    "    activation='tanh',\n",
    ")\n",
    "\n",
    "# initialize agent to the dimension of state space and number of actions\n",
    "agent.partial_fit([env.reset()] * n_actions, range(n_actions), range(n_actions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_session(env, agent, t_max=1000):\n",
    "    \"\"\"\n",
    "    Play a single game using agent neural network.\n",
    "    Terminate when game finishes or after :t_max: steps\n",
    "    \"\"\"\n",
    "    states, actions = [], []\n",
    "    total_reward = 0\n",
    "\n",
    "    s = env.reset()\n",
    "\n",
    "    for t in range(t_max):\n",
    "        \n",
    "        # use agent to predict a vector of action probabilities for state :s:\n",
    "        probs = <YOUR CODE>\n",
    "\n",
    "        assert probs.shape == (env.action_space.n,), \"make sure probabilities are a vector (hint: np.reshape)\"\n",
    "        \n",
    "        # use the probabilities you predicted to pick an action\n",
    "        # sample proportionally to the probabilities, don't just take the most likely action\n",
    "        a = <YOUR CODE>\n",
    "        # ^-- hint: try np.random.choice\n",
    "\n",
    "        new_s, r, done, info = env.step(a)\n",
    "\n",
    "        # record sessions like you did before\n",
    "        states.append(s)\n",
    "        actions.append(a)\n",
    "        total_reward += r\n",
    "\n",
    "        s = new_s\n",
    "        if done:\n",
    "            break\n",
    "    return states, actions, total_reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_states, dummy_actions, dummy_reward = generate_session(env, agent, t_max=5)\n",
    "print(\"states:\", np.stack(dummy_states))\n",
    "print(\"actions:\", dummy_actions)\n",
    "print(\"reward:\", dummy_reward)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CEM steps\n",
    "Deep CEM uses exactly the same strategy as the regular CEM, so you can copy your function code from previous notebook.\n",
    "\n",
    "The only difference is that now each observation is not a number but a `float32` vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def select_elites(states_batch, actions_batch, rewards_batch, percentile=50):\n",
    "    \"\"\"\n",
    "    Select states and actions from games that have rewards >= percentile\n",
    "    :param states_batch: list of lists of states, states_batch[session_i][t]\n",
    "    :param actions_batch: list of lists of actions, actions_batch[session_i][t]\n",
    "    :param rewards_batch: list of rewards, rewards_batch[session_i]\n",
    "\n",
    "    :returns: elite_states,elite_actions, both 1D lists of states and respective actions from elite sessions\n",
    "\n",
    "    Please return elite states and actions in their original order \n",
    "    [i.e. sorted by session number and timestep within session]\n",
    "\n",
    "    If you are confused, see examples below. Please don't assume that states are integers\n",
    "    (they will become different later).\n",
    "    \"\"\"\n",
    "\n",
    "    <YOUR CODE: copy-paste your implementation from the previous notebook>\n",
    "    \n",
    "    return elite_states, elite_actions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training loop\n",
    "Generate sessions, select N best and fit to those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import clear_output\n",
    "\n",
    "def show_progress(rewards_batch, log, percentile, reward_range=[-990, +10]):\n",
    "    \"\"\"\n",
    "    A convenience function that displays training progress. \n",
    "    No cool math here, just charts.\n",
    "    \"\"\"\n",
    "\n",
    "    mean_reward = np.mean(rewards_batch)\n",
    "    threshold = np.percentile(rewards_batch, percentile)\n",
    "    log.append([mean_reward, threshold])\n",
    "\n",
    "    clear_output(True)\n",
    "    print(\"mean reward = %.3f, threshold=%.3f\" % (mean_reward, threshold))\n",
    "    plt.figure(figsize=[8, 4])\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(list(zip(*log))[0], label='Mean rewards')\n",
    "    plt.plot(list(zip(*log))[1], label='Reward thresholds')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.hist(rewards_batch, range=reward_range)\n",
    "    plt.vlines([np.percentile(rewards_batch, percentile)],\n",
    "               [0], [100], label=\"percentile\", color='red')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_sessions = 100\n",
    "percentile = 70\n",
    "log = []\n",
    "\n",
    "for i in range(100):\n",
    "    # generate new sessions\n",
    "    sessions = [ <YOUR CODE: generate a list of n_sessions new sessions> ]\n",
    "\n",
    "    states_batch, actions_batch, rewards_batch = map(np.array, zip(*sessions))\n",
    "\n",
    "    elite_states, elite_actions = <YOUR CODE: select elite actions just like before>\n",
    "\n",
    "    <YOUR CODE: partial_fit agent to predict elite_actions(y) from elite_states(X)>\n",
    "\n",
    "    show_progress(rewards_batch, log, percentile, reward_range=[0, np.max(rewards_batch)])\n",
    "\n",
    "    if np.mean(rewards_batch) > 190:\n",
    "        print(\"You Win! You may stop training now via KeyboardInterrupt.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Record sessions\n",
    "\n",
    "import gym.wrappers\n",
    "\n",
    "with gym.wrappers.Monitor(gym.make(\"CartPole-v0\"), directory=\"videos\", force=True) as env_monitor:\n",
    "    sessions = [generate_session(env_monitor, agent) for _ in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show video. This may not work in some setups. If it doesn't\n",
    "# work for you, you can download the videos and view them locally.\n",
    "\n",
    "from pathlib import Path\n",
    "from IPython.display import HTML\n",
    "\n",
    "video_names = sorted([s for s in Path('videos').iterdir() if s.suffix == '.mp4'])\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"640\" height=\"480\" controls>\n",
    "  <source src=\"{}\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\".format(video_names[-1]))  # You can also try other indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework part I\n",
    "\n",
    "### Tabular crossentropy method\n",
    "\n",
    "You may have noticed that the taxi problem quickly converges from -100 to a near-optimal score and then descends back into -50/-100. This is in part because the environment has some innate randomness. Namely, the starting points of passenger/driver change from episode to episode.\n",
    "\n",
    "### Tasks\n",
    "- __1.1__ (1 pts) Find out how the algorithm performance changes if you use a different `percentile` and/or `n_sessions`.\n",
    "- __1.2__ (2 pts) Tune the algorithm to end up with positive average score.\n",
    "\n",
    "It's okay to modify the existing code.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```<Describe what you did here.  Preferably with plot/report to support it.>```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework part II\n",
    "\n",
    "### Deep crossentropy method\n",
    "\n",
    "By this moment you should have got enough score on [CartPole-v0](https://gym.openai.com/envs/CartPole-v0) to consider it solved (see the link). It's time to try something harder.\n",
    "\n",
    "* if you have any trouble with CartPole-v0 and feel stuck, feel free to ask us or your peers for help.\n",
    "\n",
    "### Tasks\n",
    "\n",
    "* __2.1__ (3 pts) Pick one of environments: `MountainCar-v0` or `LunarLander-v2`.\n",
    "  * For MountainCar, get average reward of __at least -150__\n",
    "  * For LunarLander, get average reward of __at least +50__\n",
    "\n",
    "See the tips section below, it's kinda important.\n",
    "__Note:__ If your agent is below the target score, you'll still get most of the points depending on the result, so don't be afraid to submit it.\n",
    "  \n",
    "  \n",
    "* __2.2__ (up to 6 pt) Devise a way to speed up training against the default version\n",
    "  * Obvious improvement: use [`joblib`](https://joblib.readthedocs.io/en/latest/). However, note that you will probably need to spawn a new environment in each of the workers instead of passing it via pickling.\n",
    "  * Try re-using samples from 3-5 last iterations when computing threshold and training.\n",
    "  * Experiment with the number of training iterations and learning rate of the neural network (see params).\n",
    "  \n",
    "__Please list what you did in Anytask submission form. You must measure your improvement experimentally. Your score depends on this improvement.__\n",
    "\n",
    "* __If the algorithm converges 2x faster, you obtain 3 pts.__\n",
    "* __If the algorithm converges 4x faster, you obtain 6 pts.__\n",
    "  \n",
    "  \n",
    "### Tips\n",
    "* Gym page: [MountainCar](https://gym.openai.com/envs/MountainCar-v0), [LunarLander](https://gym.openai.com/envs/LunarLander-v2)\n",
    "* Sessions for MountainCar may last for 10k+ ticks. Make sure ```t_max``` param is at least 10k.\n",
    " * Also it may be a good idea to cut rewards via \">\" and not \">=\". If 90% of your sessions get reward of -10k and 10% are better, than if you use percentile 20% as threshold, R >= threshold __fails cut off bad sessions__ whule R > threshold works alright.\n",
    "* _issue with gym_: Some versions of gym limit game time by 200 ticks. This will prevent cem training in most cases. Make sure your agent is able to play for the specified __t_max__, and if it isn't, try `env = gym.make(\"MountainCar-v0\").env` or otherwise get rid of TimeLimit wrapper.\n",
    "* If you use old _swig_ lib for LunarLander-v2, you may get an error. See this [issue](https://github.com/openai/gym/issues/100) for solution.\n",
    "* If it won't train it's a good idea to plot reward distribution and record sessions: they may give you some clue. If they don't, call course staff :)\n",
    "* 20-neuron network is probably not enough, feel free to experiment.\n",
    "\n",
    "You may find the following snippet useful:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def visualize_mountain_car(env, agent):\n",
    "    # Compute policy for all possible x and v (with discretization)\n",
    "    xs = np.linspace(env.min_position, env.max_position, 100)\n",
    "    vs = np.linspace(-env.max_speed, env.max_speed, 100)\n",
    "    \n",
    "    grid = np.dstack(np.meshgrid(xs, vs[::-1])).transpose(1, 0, 2)\n",
    "    grid_flat = grid.reshape(len(xs) * len(vs), 2)\n",
    "    probs = agent.predict_proba(grid_flat).reshape(len(xs), len(vs), 3).transpose(1, 0, 2)\n",
    "\n",
    "    # # The above code is equivalent to the following:\n",
    "    # probs = np.empty((len(vs), len(xs), 3))\n",
    "    # for i, v in enumerate(vs[::-1]):\n",
    "    #     for j, x in enumerate(xs):\n",
    "    #         probs[i, j, :] = agent.predict_proba([[x, v]])[0]\n",
    "\n",
    "    # Draw policy\n",
    "    f, ax = plt.subplots(figsize=(7, 7))\n",
    "    ax.imshow(probs, extent=(env.min_position, env.max_position, -env.max_speed, env.max_speed), aspect='auto')\n",
    "    ax.set_title('Learned policy: red=left, green=nothing, blue=right')\n",
    "    ax.set_xlabel('position (x)')\n",
    "    ax.set_ylabel('velocity (v)')\n",
    "    \n",
    "    # Sample a trajectory and draw it\n",
    "    states, actions, _ = generate_session(env, agent)\n",
    "    states = np.array(states)\n",
    "    ax.plot(states[:, 0], states[:, 1], color='white')\n",
    "    \n",
    "    # Draw every 3rd action from the trajectory\n",
    "    for (x, v), a in zip(states[::3], actions[::3]):\n",
    "        if a == 0:\n",
    "            plt.arrow(x, v, -0.1, 0, color='white', head_length=0.02)\n",
    "        elif a == 2:\n",
    "            plt.arrow(x, v, 0.1, 0, color='white', head_length=0.02)\n",
    "\n",
    "with gym.make('MountainCar-v0').env as env:\n",
    "    visualize_mountain_car(env, agent_mountain_car)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bonus tasks\n",
    "\n",
    "* __2.3 bonus__ (2 pts) Try to find a network architecture and training params that solve __both__ environments above (_Points depend on implementation. If you attempted this task, please mention it in Anytask submission._)\n",
    "\n",
    "* __2.4 bonus__ (4 pts) Solve continuous action space task with `MLPRegressor` or similar.\n",
    "  * Since your agent only predicts the \"expected\" action, you will have to add noise to ensure exploration.\n",
    "  * Choose one of [MountainCarContinuous-v0](https://gym.openai.com/envs/MountainCarContinuous-v0) (90+ pts to solve), [LunarLanderContinuous-v2](https://gym.openai.com/envs/LunarLanderContinuous-v2) (200+ pts to solve) \n",
    "  * 4 points for solving. Slightly less for getting some results below solution threshold. Note that discrete and continuous environments may have slightly different rules aside from action spaces.\n",
    "\n",
    "\n",
    "If you're still feeling unchallenged, consider the project (see other notebook in this folder)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python",
   "pygments_lexer": "ipython3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}