{ "metadata": { "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.0" }, "orig_nbformat": 2, "kernelspec": { "name": "python3", "display_name": "Python 3.7.0 64-bit ('3.7')" }, "interpreter": { "hash": "70b38d7a306a849643e446cd70466270a13445e5987dfa1344ef2b127438fa4d" } }, "nbformat": 4, "nbformat_minor": 2, "cells": [ { "source": [ "# Peter and the Wolf: Reinforcement Learning Primer\n", "\n", "In this tutorial, we will learn how to apply Reinforcement learning to a problem of path finding. The setting is inspired by [Peter and the Wolf](https://en.wikipedia.org/wiki/Peter_and_the_Wolf) musical fairy tale by Russian composer [Sergei Prokofiev](https://en.wikipedia.org/wiki/Sergei_Prokofiev). It is a story about young pioneer Peter, who bravely goes out of his house to the forest clearing to chase a wolf. We will train machine learning algorithms that will help Peter to explore the surrounding area and build an optimal navigation map.\n", "\n", "First, let's import a bunch of useful libraries:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import random\n", "import math" ] }, { "source": [ "## Overview of Reinforcement Learning\n", "\n", "**Reinforcement Learning** (RL) is a learning technique that allows us to learn an optimal behaviour of an **agent** in some **environment** by running many experiments. An agent in this environment should have some **goal**, defined by a **reward function**.\n", "\n", "## The Environment\n", "\n", "For simplicity, let's consider Peter's world to be a square board of size `width` x `height`. Each cell in this board can either be:\n", "* **ground**, on which Peter and other creatures can walk\n", "* **water**, on which you obviously cannot walk\n", "* **a tree** or **grass** - a place where you can rest\n", "* **an apple**, which represents something Peter would be glad to find in order to feed himself\n", "* **a wolf**, which is dangerous and should be avoided\n", "\n", "To work with the environment, we will define a class called `Board`. In order not to clutter this notebook too much, we have moved all code to work with the board into separate `rlboard` module, which we will now import. You may look inside this module to get more details about the internals of the implementation." ], "cell_type": "markdown", "metadata": {} }, { "source": [ "Let's now create a random board and see how it looks:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# code block 1" ] }, { "source": [ "## Actions and Policy\n", "\n", "In our example, Peter's goal would be to find an apple, while avoiding the wolf and other obstacles. Define those actions as a dictionary, and map them to pairs of corresponding coordinate changes." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# code block 2" ] }, { "source": [ "The strategy of our agent (Peter) is defined by a so-called **policy**. Let's consider the simplest policy called **random walk**.\n", "\n", "## Random walk\n", "\n", "Let's first solve our problem by implementing a random walk strategy." ], "cell_type": "markdown", "metadata": {} }, { "source": [ "# Let's run a random walk experiment several times and see the average number of steps taken: code block 3" ], "cell_type": "code", "metadata": {}, "execution_count": null, "outputs": [] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# code block 4" ] }, { "source": [ "## Reward Function\n", "\n", "To make our policy more intelligent, we need to understand which moves are \"better\" than others.\n", "\n" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "#code block 5" ] }, { "source": [ "## Q-Learning\n", "\n", "Build a Q-Table, or multi-dimensional array. Since our board has dimentions `width` x `height`, we can represent Q-Table by a numpy array with shape `width` x `height` x `len(actions)`:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# code block 6" ] }, { "source": [ "Pass the Q-Table to the `plot` function in order to visualize the table on the board:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "output_type": "error", "ename": "NameError", "evalue": "name 'm' is not defined", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'm' is not defined" ] } ], "source": [ "m.plot(Q)" ] }, { "source": [ "\n", "## Essence of Q-Learning: Bellman Equation and Learning Algorithm\n", "\n", "Write a pseudo-code for our leaning algorithm:\n", "\n", "* Initialize Q-Table Q with equal numbers for all states and actions\n", "* Set learning rate $\\alpha\\leftarrow 1$\n", "* Repeat simulation many times\n", " 1. Start at random position\n", " 1. Repeat\n", " 1. Select an action $a$ at state $s$\n", " 2. Exectute action by moving to a new state $s'$\n", " 3. If we encounter end-of-game condition, or total reward is too small - exit simulation \n", " 4. Compute reward $r$ at the new state\n", " 5. Update Q-Function according to Bellman equation: $Q(s,a)\\leftarrow (1-\\alpha)Q(s,a)+\\alpha(r+\\gamma\\max_{a'}Q(s',a'))$\n", " 6. $s\\leftarrow s'$\n", " 7. Update total reward and decrease $\\alpha$.\n", "\n", "## Exploit vs. Explore\n", "\n", "The best approach is to balance between exploration and exploitation. As we learn more about our environment, we would be more likely to follow the optimal route, however, choosing the unexplored path once in a while.\n", "\n", "## Python Implementation\n", "\n", "Now we are ready to implement the learning algorithm. Before that, we also need some function that will convert arbitrary numbers in the Q-Table into a vector of probabilities for corresponding actions:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# code block 7" ] }, { "source": [ "We add a small amount of `eps` to the original vector in order to avoid division by 0 in the initial case, when all components of the vector are identical.\n", "\n", "The actual learning algorithm we will run for 5000 experiments, also called **epochs**: " ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "" ] } ], "source": [ "\n", "from IPython.display import clear_output\n", "\n", "lpath = []\n", "\n", "# code block 8" ] }, { "source": [ "After executing this algorithm, the Q-Table should be updated with values that define the attractiveness of different actions at each step. Visualize the table here:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "m.plot(Q)" ] }, { "source": [ "## Checking the Policy\n", "\n", "Since Q-Table lists the \"attractiveness\" of each action at each state, it is quite easy to use it to define the efficient navigation in our world. In the simplest case, we can just select the action corresponding to the highest Q-Table value:" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "2" ] }, "metadata": {}, "execution_count": 13 } ], "source": [ "# code block 9" ] }, { "source": [ "If you try the code above several times, you may notice that sometimes it just \"hangs\", and you need to press the STOP button in the notebook to interrupt it. \n", "\n", "> **Task 1:** Modify the `walk` function to limit the maximum length of path by a certain number of steps (say, 100), and watch the code above return this value from time to time.\n", "\n", "> **Task 2:** Modify the `walk` function so that it does not go back to the places where is has already been previously. This will prevent `walk` from looping, however, the agent can still end up being \"trapped\" in a location from which it is unable to escape." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Average path length = 5.31, eaten by wolf: 0 times\n" ] } ], "source": [ "\n", "# code block 10" ] }, { "source": [ "## Investigating the Learning Process" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[]" ] }, "metadata": {}, "execution_count": 57 }, { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "plt.plot(lpath)" ] }, { "source": [ "## Exercise\n", "## A more realistic Peter and the Wolf world\n", "\n", "\n" ], "cell_type": "markdown", "metadata": {} } ] }