S66_driving_DRL.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github",
    "tags": [
     "no-tex"
    ]
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S66_driving_DRL.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "JoW4C_OkOMhe",
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -U gtbook\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "10-snNDwOSuC",
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import plotly.express as px\n",
    "\n",
    "try:\n",
    "    import google.colab\n",
    "except:\n",
    "    import plotly.io as pio\n",
    "    pio.renderers.default = \"png\""
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "id": "nAvx4-UCNzt2"
   },
   "source": [
    "# Deep Reinforcement Learning\n",
    "\n",
    "> Deep Q-learning and policy gradient.\n",
    "\n",
    "<img src=\"Figures6/S66-Autonomous_Vehicle_with_LIDAR_and_cameras-03.jpg\" alt=\"Splash image with steampunk autonomous car\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">\n",
    "\n",
    "Deep reinforcement learning brings the power of deep learning to much more complex domains than what we were able to tackle with the Markov Decision Processes and RL concepts introduced in Chapter 3. The use of large, expressive neural networks has allowed researchers and practitioners alike to work with high bandwidth sensors such as video streams and LIDAR, and bring the promise of RL into real-world domains such as autonomous driving. This is still a field of active discovery and research, however, and we can give but a brief introduction here about what is a vast literature and problem space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RL and Autonomous Driving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: A 3-lane highway.\n",
    "#| label: fig:highway\n",
    "px.line(x=[0, 1, 2, 3], y=[1, 3, 2, 4], labels={'x': 'x-axis', 'y': 'y-axis'}, title='3-lane highway')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An simple example in the autonomous driving domain is *lane switching*. Suppose we are driving along at 3-lane highway, and we can see some ways ahead, and some ways behind us. We are driving at a speed that is comfortable to us, but other cars have different ideas about the optimal speed to drive at. Hence, sometimes we would like to change lanes, and we could learn a policy to do this for us. This is called **lateral control**. A more sophisticated example would also allow us to adapt our speed to the traffic pattern, but by relying on a smart cruise control system we could safely ignore this **longitudinal control** problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To turn this into a reinforcement learning problem, we first need to define a state space ${\\cal X}$ and an action space ${\\cal A}$. There are a variety of ways to engineer this aspect of the problem. For example, we could somehow encode the longitudinal distance to the lane index for each of the K closest cars, where K is a parameter, say 5 or 10. One problem is that the number of cars that are *actually* present is variable, which is difficult to deal with. Another approach is to make this into an image processing problem, by creating a finite element representation of the road before and behind us, and marking a cell as occupied or not. The latter is fairly compatible with automotive sensors such as LIDAR."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Figure with actions LEFT, RIGHT, STAY.\n",
    "#| label: fig:actions\n",
    "px.line(x=[0, 1, 2, 3], y=[1, 3, 2, 4], labels={'x': 'x-axis', 'y': 'y-axis'}, title='LEFT, RIGHT, STAY')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In terms of actions, the easiest approach is to have a number of discrete choices to go `left`, `right`, or `stay` in the current lane. We could be more sophisticated about it and have both \"aggressive\" and \"slow\" versions of these in addition to a default version, akin to the motion primitives previously discussed.\n",
    "\n",
    "Actually implementing this on an autonomous vehicle, or even sketching an implementation in a notebook with recorded or simulated data, is beyond what we can accomplish in a notebook. Hence, we will be content below to sketch three popular foundational methods from deep reinforcement learning, without actually implementing them here. At the end of this chapter we provide some references where you can delve into these topics more deeply."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deep Q-Learning\n",
    "\n",
    "> DQN is an early deep learning RL method akin to Q-learning.\n",
    "\n",
    "Recall from Section 3.6 that we can define a policy in terms of **Q-values**, sometimes also called state-action values, and that we can define the optimal policy as \n",
    "\n",
    "$$\n",
    "\\pi^*(x) = \\arg \\max_a Q^*(x,a)\n",
    "$$\n",
    "\n",
    "In Q-learning, we start with some random Q-values and then gradually estimate the optimal Q-values by alpha-blending between old and new estimates:\n",
    "\n",
    "$$\n",
    "\\hat{Q}(x,a) \\leftarrow (1-\\alpha) \\hat{Q}(x,a) + \\alpha~\\text{target}(x,a,x')\n",
    "$$\n",
    "\n",
    "where $\\text{target}(x,a,x') \\doteq R(x,a,x') + \\gamma \\max_{a'} \\hat{Q}(x',a')$ is the \"target\" value that we think is an improvment on the previous value $\\hat{Q}(x,a)$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the **deep Q-network** or DQN method we use a *supervised learning* approach to Q-learning, by training a neural network, parameterized by $\\theta$, to approximate the optimal Q-values:\n",
    "\n",
    "$$\n",
    "Q^*(x,a) \\approx Q(x,a; \\theta)\n",
    "$$\n",
    "\n",
    "DQN as a method uses two additional ideas that are crucial in making the training converge to something sensible in difficult problems. The first is splitting the training into *execution* and *experience replay* phases:\n",
    "\n",
    "- during the **execution phase**, it executes the policy (possibly with some degree of randomness) and stores the experiences $(x,a,r,x')$, with $r$ the reward, in a dataset $D$;\n",
    "- during **experience replay**, it *randomly samples* from these experiences to create mini-batches of data, which are in turn used to perform stochastic gradient descent on the parameters $\\theta$.\n",
    "\n",
    "The second is to calculate the target values $\\text{target}(x,a,x') \\doteq R(x,a,x') + \\gamma \\max_{a'} \\hat{Q}(x',a'; \\theta^{old})$ with the parameters $\\theta^{old}$ from the previous epoch, to provide a more stable approximation target.\n",
    "\n",
    "With this basic scheme, a team from DeepMind was able to achieve human or super-human performance on about 50 Atari 2600 games in 2015 (Minh et al., Nature 2015, Vol. 518)."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Policy Optimization\n",
    "\n",
    "> Policy optimization takes a black box optimization approach to a deep policy.\n",
    "\n",
    "We can use a deep neural network, parameterized by $\\theta$, to encode a **stochastic policy**:\n",
    "\n",
    "$$\n",
    "\\pi(a|x, \\theta)\n",
    "$$\n",
    "\n",
    "where $a \\in {\\cal A}$ is an action, $x \\in {\\cal X}$ is a state, and the policy outputs a *probability* for each action $a$ based on the state $x$.\n",
    "\n",
    "Similar to policy iteration, policy optimization tries to find the policy $\\pi$ that maximizes the expected utility. One way to estimate this quantity is to do a rollout for a finite horizon $H$, as we discussed in Chapter 3. An often used loss function when stochastic policy parameters $\\theta$ being optimized for is\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(\\theta) = \\sum_{t=0}^H R_t - \\log \\pi(a_t|x_t, \\theta)\n",
    "$$\n",
    "\n",
    "where $R^t$ is the expected return for the $t^{th}$ transition in the rollout, and is computed as\n",
    "\n",
    "$$\n",
    "R^t \\doteq \\sum_{k=t}^H \\gamma^{k-t}R(x_t,a_t,x_{t+1})\n",
    "$$\n",
    "\n",
    "The reason to use $\\log \\pi(a_t|x_t, \\theta)$"
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   "cell_type": "markdown",
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   "source": [
    "A very simple optimization method is **hill climbing**:\n",
    "\n",
    "- initialize $\\theta$ and compute $\\mathcal{L}(\\theta)$.\n",
    "- until convergence:\n",
    "    - perturb $\\theta$ to $\\theta'$\n",
    "    - if $\\mathcal{L}(\\theta') < \\mathcal{L}(\\theta)$:\n",
    "        - set $\\theta \\leftarrow \\theta`$\n",
    "\n",
    "Above the *perturbation* step could be as simple as adding some Gaussian noise to the weights of the network.\n",
    "\n",
    "More sophisticated \"black-box\" approaches such as genetic algorithms or evolution strategies can be applied to this problem instead, but they all share the property that they are \"gradient-free\", which seems to be a sub-optimal strategy. Hence, we next look at a gradient descent approach to policy optimization."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Policy Gradient\n",
    "\n",
    "> Policy gradient methods are akin to policy iteration, with a deep twist.\n",
    "\n",
    "In a nutshell, policy gradient calculates the gradient of the loss with respect to the policy parameters $\\theta$:\n",
    "\n",
    "$$\n",
    "\\nabla_\\theta \\mathcal{L}(\\theta) \\leftarrow \\sum_{t=0}^H - R_t \\nabla_\\theta \\log \\pi(a_t|x_t, \\theta)\n",
    "$$\n",
    "\n",
    "and then uses gradient descent to update the policy parameters:\n",
    "\n",
    "$$\n",
    "\\theta \\leftarrow \\theta - \\alpha \\nabla_\\theta \\mathcal{L}(\\theta)\n",
    "$$\n",
    "\n",
    "where $\\alpha$ is a learning rate.\n",
    "\n",
    "There are a whole host of reasons why the above, vanilla **policy gradient algorithm**, does not work well. Hence, there is a large variety of methods that try to improve the performance of this algorithm, beginning with the 1992 REINFORCE method (Williams, 1992), up to more modern methods such as PPO, which is now one of the most often-used methods.\n"
   ]
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