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404 lines
291 KiB
404 lines
291 KiB
{
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"metadata": {
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.0"
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},
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"orig_nbformat": 2,
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3.7.0 64-bit ('3.7')"
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},
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"interpreter": {
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"hash": "70b38d7a306a849643e446cd70466270a13445e5987dfa1344ef2b127438fa4d"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2,
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"cells": [
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{
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"source": [
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"# Peter and the Wolf: Reinforcement Learning Primer\n",
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"\n",
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"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",
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"\n",
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"First, let's import a bunch of useful libraries:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import random\n",
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"import math"
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]
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},
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{
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"source": [
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"## Overview of Reinforcement Learning\n",
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"\n",
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"**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",
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"\n",
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"## The Environment\n",
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"\n",
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"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",
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"* **ground**, on which Peter and other creatures can walk\n",
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"* **water**, on which you obviously cannot walk\n",
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"* **a tree** or **grass** - a place where you can rest\n",
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"* **an apple**, which represents something Peter would be glad to find in order to feed himself\n",
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"* **a wolf**, which is dangerous and should be avoided\n",
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"\n",
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"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."
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"source": [
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"Let's now create a random board and see how it looks:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"# code block 1"
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]
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},
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{
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"source": [
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"## Actions and Policy\n",
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"\n",
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"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."
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"# code block 2"
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]
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},
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{
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"source": [
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"The strategy of our agent (Peter) is defined by a so-called **policy**. Let's consider the simplest policy called **random walk**.\n",
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"\n",
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"## Random walk\n",
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"\n",
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"Let's first solve our problem by implementing a random walk strategy."
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"source": [
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"# Let's run a random walk experiment several times and see the average number of steps taken: code block 3"
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],
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"cell_type": "code",
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"metadata": {},
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"# code block 4"
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]
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},
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{
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"source": [
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"## Reward Function\n",
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"\n",
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"To make our policy more intelligent, we need to understand which moves are \"better\" than others.\n",
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"\n"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"#code block 5"
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]
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},
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{
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"source": [
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"## Q-Learning\n",
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"\n",
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"Build a Q-Table, or multi-dimensional array. Since our board has dimensions `width` x `height`, we can represent Q-Table by a numpy array with shape `width` x `height` x `len(actions)`:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"# code block 6"
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]
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},
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{
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"source": [
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"Pass the Q-Table to the `plot` function in order to visualize the table on the board:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"output_type": "error",
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"ename": "NameError",
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"evalue": "name 'm' is not defined",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-10-8b8a9e4cb2b8>\u001b[0m in \u001b[0;36m<module>\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",
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"\u001b[0;31mNameError\u001b[0m: name 'm' is not defined"
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]
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}
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],
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"source": [
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"m.plot(Q)"
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]
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},
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{
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"source": [
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"\n",
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"## Essence of Q-Learning: Bellman Equation and Learning Algorithm\n",
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"\n",
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"Write a pseudo-code for our leaning algorithm:\n",
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"\n",
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"* Initialize Q-Table Q with equal numbers for all states and actions\n",
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"* Set learning rate $\\alpha\\leftarrow 1$\n",
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"* Repeat simulation many times\n",
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" 1. Start at random position\n",
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" 1. Repeat\n",
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" 1. Select an action $a$ at state $s$\n",
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" 2. Exectute action by moving to a new state $s'$\n",
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" 3. If we encounter end-of-game condition, or total reward is too small - exit simulation \n",
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" 4. Compute reward $r$ at the new state\n",
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" 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",
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" 6. $s\\leftarrow s'$\n",
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" 7. Update total reward and decrease $\\alpha$.\n",
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"\n",
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"## Exploit vs. Explore\n",
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"\n",
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"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",
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"\n",
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"## Python Implementation\n",
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"\n",
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"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:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"# code block 7"
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]
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},
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{
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"source": [
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"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",
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"\n",
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"The actual learning algorithm we will run for 5000 experiments, also called **epochs**: "
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 56,
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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""
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]
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}
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],
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"source": [
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"\n",
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"from IPython.display import clear_output\n",
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"\n",
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"lpath = []\n",
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"\n",
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"# code block 8"
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]
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},
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{
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"source": [
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"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:"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 43,
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"metadata": {},
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"outputs": [
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{
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"output_type": "display_data",
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"data": {
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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": {
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|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x26dab295a48>]"
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|
]
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|
},
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|
"metadata": {},
|
|
"execution_count": 57
|
|
},
|
|
{
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|
"output_type": "display_data",
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|
"data": {
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"text/plain": "<Figure size 432x288 with 1 Axes>",
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109.263403 214.085931 \r\nL 109.293843 201.703888 \r\nL 109.385161 202.919046 \r\nL 109.44604 214.756364 \r\nL 109.476479 192.192132 \r\nL 109.537358 214.735413 \r\nL 109.598237 214.756364 \r\nL 109.719994 198.100315 \r\nL 109.811312 214.756364 \r\nL 109.841752 210.230947 \r\nL 109.872191 214.735413 \r\nL 109.93307 208.63867 \r\nL 110.054828 214.756364 \r\nL 110.085267 200.509681 \r\nL 110.146146 208.052042 \r\nL 110.207025 214.756364 \r\nL 110.267904 213.268842 \r\nL 110.298343 193.470143 \r\nL 110.328782 214.756364 \r\nL 110.359222 209.811927 \r\nL 110.420101 214.756364 \r\nL 110.480979 214.044029 \r\nL 110.541858 214.756364 \r\nL 110.572298 212.032733 \r\nL 110.633176 214.756364 \r\nL 110.663616 214.756364 \r\nL 110.694055 199.441179 \r\nL 110.785374 202.981899 \r\nL 110.907131 214.756364 \r\nL 110.937571 211.110889 \r\nL 110.998449 214.756364 \r\nL 111.089768 209.916682 \r\nL 111.181086 214.756364 \r\nL 111.211525 203.882792 \r\nL 111.272404 207.842532 \r\nL 111.302843 214.756364 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115.046891 214.46305 \r\nL 115.07733 207.339708 \r\nL 115.168648 209.66527 \r\nL 115.229527 213.268842 \r\nL 115.290406 211.215644 \r\nL 115.320845 205.642677 \r\nL 115.351285 214.756364 \r\nL 115.381724 209.749074 \r\nL 115.533921 214.756364 \r\nL 115.564361 213.687862 \r\nL 115.655679 206.606423 \r\nL 115.746997 214.756364 \r\nL 115.716558 193.700604 \r\nL 115.777436 214.735413 \r\nL 115.838315 193.763457 \r\nL 115.868755 193.910114 \r\nL 115.899194 214.756364 \r\nL 115.990512 212.346998 \r\nL 116.051391 210.754722 \r\nL 116.11227 214.756364 \r\nL 116.142709 211.76037 \r\nL 116.203588 214.756364 \r\nL 116.234027 214.756364 \r\nL 116.264467 213.478352 \r\nL 116.294906 214.756364 \r\nL 116.325346 184.670721 \r\nL 116.386225 214.756364 \r\nL 116.416664 214.044029 \r\nL 116.447103 214.756364 \r\nL 116.477543 196.047117 \r\nL 116.538422 212.786969 \r\nL 116.5993 210.964232 \r\nL 116.690619 214.756364 \r\nL 116.812376 200.404926 \r\nL 116.903694 214.756364 \r\nL 116.934134 196.403284 \r\nL 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213.059332 \r\nL 126.705184 214.756364 \r\nL 126.735623 192.192132 \r\nL 126.796502 213.750715 \r\nL 126.91826 214.756364 \r\nL 126.979138 210.021437 \r\nL 127.009578 214.756364 \r\nL 127.040017 214.756364 \r\nL 127.131335 210.461408 \r\nL 127.192214 207.402561 \r\nL 127.253093 214.756364 \r\nL 127.283532 210.377604 \r\nL 127.344411 214.735413 \r\nL 127.374851 214.756364 \r\nL 127.40529 214.46305 \r\nL 127.466169 214.756364 \r\nL 127.527048 199.524983 \r\nL 127.557487 214.735413 \r\nL 127.587927 211.404203 \r\nL 127.618366 177.673086 \r\nL 127.648805 214.756364 \r\nL 127.679245 184.251701 \r\nL 127.801002 214.756364 \r\nL 127.861881 214.756364 \r\nL 127.953199 207.612071 \r\nL 128.014078 214.756364 \r\nL 128.044518 204.532273 \r\nL 128.074957 198.309825 \r\nL 128.105396 214.756364 \r\nL 128.166275 214.756364 \r\nL 128.257593 210.105241 \r\nL 128.348912 214.756364 \r\nL 128.501109 186.430606 \r\nL 128.531548 210.314751 \r\nL 128.592427 206.459766 \r\nL 128.622866 168.349889 \r\nL 128.683745 214.756364 \r\nL 128.714185 214.756364 \r\nL 128.744624 209.749074 \r\nL 128.805503 214.358295 \r\nL 128.835942 214.756364 \r\nL 128.866382 204.993196 \r\nL 128.9577 205.977893 \r\nL 128.988139 214.756364 \r\nL 129.018579 179.537725 \r\nL 129.079457 205.726481 \r\nL 129.170776 214.756364 \r\nL 129.140336 194.727203 \r\nL 129.201215 214.735413 \r\nL 129.231655 214.756364 \r\nL 129.262094 214.169736 \r\nL 129.292533 207.716826 \r\nL 129.322973 214.756364 \r\nL 129.353412 214.756364 \r\nL 129.383852 214.756364 \r\nL 129.414291 214.085931 \r\nL 129.44473 214.358295 \r\nL 129.505609 162.253146 \r\nL 129.536049 191.982622 \r\nL 129.566488 214.735413 \r\nL 129.657806 202.981899 \r\nL 129.688246 193.093025 \r\nL 129.718685 214.756364 \r\nL 129.779564 214.756364 \r\nL 129.810003 188.441902 \r\nL 129.870882 213.164087 \r\nL 129.99264 205.223657 \r\nL 129.931761 214.714462 \r\nL 130.053519 206.166452 \r\nL 130.144837 214.756364 \r\nL 130.175276 214.693511 \r\nL 130.236155 214.735413 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203.568527 \r\nL 132.458232 214.400197 \r\nL 132.488671 202.122908 \r\nL 132.519111 214.714462 \r\nL 132.54955 209.749074 \r\nL 132.671308 214.756364 \r\nL 132.701747 214.735413 \r\nL 132.732186 181.046197 \r\nL 132.793065 214.756364 \r\nL 132.884383 214.756364 \r\nL 132.914823 212.870773 \r\nL 132.945262 214.756364 \r\nL 132.975702 195.942362 \r\nL 133.03658 209.895731 \r\nL 133.06702 213.918323 \r\nL 133.097459 196.214725 \r\nL 133.127899 214.756364 \r\nL 133.158338 199.797346 \r\nL 133.280096 214.735413 \r\nL 133.310535 208.63867 \r\nL 133.340975 209.225298 \r\nL 133.371414 167.260436 \r\nL 133.401853 214.756364 \r\nL 133.432293 214.756364 \r\nL 133.462732 202.730487 \r\nL 133.55405 210.08429 \r\nL 133.645369 214.756364 \r\nL 133.614929 205.600775 \r\nL 133.675808 213.876421 \r\nL 133.736687 214.756364 \r\nL 133.767126 214.735413 \r\nL 133.888884 201.515329 \r\nL 133.828005 214.756364 \r\nL 133.919323 203.861841 \r\nL 133.980202 214.735413 \r\nL 134.010642 214.400197 \r\nL 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211.215644 \r\nL 159.092713 214.756364 \r\nL 159.153592 198.540286 \r\nL 159.184032 214.756364 \r\nL 159.214471 214.756364 \r\nL 159.27535 196.780402 \r\nL 159.305789 208.701523 \r\nL 159.336229 214.756364 \r\nL 159.397107 207.444463 \r\nL 159.427547 211.13184 \r\nL 159.488426 214.756364 \r\nL 159.549304 213.541205 \r\nL 159.579744 172.644845 \r\nL 159.610183 214.756364 \r\nL 159.671062 198.435531 \r\nL 159.76238 214.756364 \r\nL 159.823259 214.609707 \r\nL 159.853699 207.612071 \r\nL 159.914577 214.756364 \r\nL 160.005896 214.735413 \r\nL 160.158093 197.953658 \r\nL 160.249411 214.756364 \r\nL 160.31029 177.233115 \r\nL 160.371168 209.770025 \r\nL 160.432047 207.716826 \r\nL 160.492926 214.756364 \r\nL 160.523366 214.735413 \r\nL 160.553805 175.640838 \r\nL 160.614684 214.756364 \r\nL 160.645123 214.609707 \r\nL 160.675563 213.01743 \r\nL 160.706002 214.756364 \r\nL 160.736441 214.756364 \r\nL 160.858199 187.310548 \r\nL 160.979957 214.756364 \r\nL 161.101714 214.756364 \r\nL 161.193032 214.756364 \r\nL 161.223472 163.300697 \r\nL 161.284351 203.191409 \r\nL 161.436548 214.756364 \r\nL 161.527866 203.149507 \r\nL 161.558305 210.314751 \r\nL 161.588745 213.520254 \r\nL 161.619184 179.705333 \r\nL 161.680063 214.190687 \r\nL 161.710502 214.735413 \r\nL 161.740942 183.099396 \r\nL 161.83226 200.467779 \r\nL 161.862699 201.075358 \r\nL 161.954018 214.756364 \r\nL 161.923578 197.974609 \r\nL 161.984457 211.13184 \r\nL 162.014896 211.571811 \r\nL 162.045336 214.337344 \r\nL 162.075775 183.371759 \r\nL 162.106215 214.756364 \r\nL 162.136654 198.121266 \r\nL 162.227972 214.756364 \r\nL 162.258412 212.870773 \r\nL 162.319291 212.786969 \r\nL 162.380169 214.756364 \r\nL 162.441048 214.588756 \r\nL 162.471488 214.735413 \r\nL 162.501927 212.619361 \r\nL 162.532366 214.274491 \r\nL 162.562806 186.011585 \r\nL 162.593245 214.756364 \r\nL 162.623685 208.512964 \r\nL 162.715003 214.756364 \r\nL 162.745442 214.735413 \r\nL 162.83676 214.756364 \r\nL 162.897639 198.016511 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213.520254 \r\nL 164.632686 213.64596 \r\nL 164.663125 208.827229 \r\nL 164.693564 214.756364 \r\nL 164.724004 209.937633 \r\nL 164.815322 214.756364 \r\nL 164.90664 193.658702 \r\nL 164.93708 202.143859 \r\nL 165.058837 214.756364 \r\nL 165.089277 214.735413 \r\nL 165.180595 214.756364 \r\nL 165.211034 195.544293 \r\nL 165.271913 210.461408 \r\nL 165.393671 214.756364 \r\nL 165.42411 196.675647 \r\nL 165.484989 204.071351 \r\nL 165.545868 214.735413 \r\nL 165.576307 199.504032 \r\nL 165.667625 208.994837 \r\nL 165.728504 214.756364 \r\nL 165.758944 212.221292 \r\nL 165.819822 192.317838 \r\nL 165.880701 206.313109 \r\nL 166.032898 214.756364 \r\nL 166.154656 198.770747 \r\nL 166.245974 214.756364 \r\nL 166.276414 208.764376 \r\nL 166.306853 214.756364 \r\nL 166.337292 200.635387 \r\nL 166.367732 208.031091 \r\nL 166.398171 192.77876 \r\nL 166.45905 214.756364 \r\nL 166.702565 214.756364 \r\nL 166.733005 185.005937 \r\nL 166.793883 186.221096 \r\nL 166.824323 214.735413 \r\nL 166.915641 208.554866 \r\nL 166.946081 214.756364 \r\nL 166.97652 214.002127 \r\nL 167.006959 195.711901 \r\nL 167.098278 201.74579 \r\nL 167.189596 214.756364 \r\nL 167.220035 209.560515 \r\nL 167.250475 209.853829 \r\nL 167.311353 214.756364 \r\nL 167.341793 184.272652 \r\nL 167.402672 210.356653 \r\nL 167.433111 214.735413 \r\nL 167.49399 214.756364 \r\nL 167.554869 188.525706 \r\nL 167.646187 214.148785 \r\nL 167.676626 208.533915 \r\nL 167.707066 214.756364 \r\nL 167.737505 195.523342 \r\nL 167.798384 213.64596 \r\nL 167.889702 198.519335 \r\nL 167.950581 201.976251 \r\nL 168.041899 214.756364 \r\nL 168.072339 210.419506 \r\nL 168.102778 211.299448 \r\nL 168.133217 210.796624 \r\nL 168.163657 192.862564 \r\nL 168.194096 214.756364 \r\nL 168.224536 199.441179 \r\nL 168.285414 214.756364 \r\nL 168.346293 210.629016 \r\nL 168.407172 190.956023 \r\nL 168.437611 204.888441 \r\nL 168.52893 214.756364 \r\nL 168.559369 214.735413 \r\nL 168.589809 199.88115 \r\nL 168.650687 214.756364 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214.756364 \r\nL 171.116279 197.597491 \r\nL 171.207598 214.756364 \r\nL 171.238037 201.159162 \r\nL 171.298916 205.894089 \r\nL 171.359795 214.756364 \r\nL 171.420673 214.190687 \r\nL 171.451113 214.756364 \r\nL 171.511992 210.314751 \r\nL 171.57287 213.164087 \r\nL 171.60331 214.756364 \r\nL 171.633749 213.352646 \r\nL 171.664189 190.599855 \r\nL 171.725068 214.735413 \r\nL 171.846825 200.530632 \r\nL 171.907704 213.268842 \r\nL 171.938143 192.56925 \r\nL 171.999022 205.621726 \r\nL 172.029462 206.522619 \r\nL 172.09034 195.334782 \r\nL 172.151219 214.756364 \r\nL 172.242537 206.187403 \r\nL 172.272977 211.55086 \r\nL 172.303416 208.492013 \r\nL 172.333856 210.901379 \r\nL 172.364295 188.420951 \r\nL 172.425174 209.811927 \r\nL 172.455613 214.546854 \r\nL 172.486053 210.985183 \r\nL 172.546932 214.756364 \r\nL 172.60781 194.119624 \r\nL 172.760007 214.756364 \r\nL 172.820886 199.839248 \r\nL 172.851326 214.756364 \r\nL 172.881765 214.756364 \r\nL 172.973083 173.776199 \r\nL 173.064401 214.756364 \r\nL 173.094841 212.095586 \r\nL 173.12528 186.744871 \r\nL 173.15572 214.756364 \r\nL 173.186159 213.164087 \r\nL 173.216598 213.352646 \r\nL 173.277477 214.735413 \r\nL 173.368796 214.756364 \r\nL 173.399235 165.521503 \r\nL 173.520993 214.756364 \r\nL 173.551432 214.756364 \r\nL 173.581871 209.05769 \r\nL 173.64275 212.032733 \r\nL 173.67319 214.756364 \r\nL 173.703629 164.997728 \r\nL 173.764508 204.783686 \r\nL 173.794947 214.756364 \r\nL 173.886265 211.027085 \r\nL 174.008023 214.756364 \r\nL 174.038462 214.756364 \r\nL 174.16022 193.6168 \r\nL 174.251538 214.756364 \r\nL 174.281978 213.205989 \r\nL 174.342857 214.756364 \r\nL 174.464614 191.333141 \r\nL 174.555932 214.756364 \r\nL 174.586372 210.775673 \r\nL 174.647251 208.890082 \r\nL 174.708129 214.756364 \r\nL 174.738569 209.162445 \r\nL 174.769008 183.099396 \r\nL 174.799448 214.756364 \r\nL 174.829887 196.235676 \r\nL 174.951645 214.756364 \r\nL 174.982084 208.722474 \r\nL 175.042963 214.546854 \r\nL 175.073402 213.289793 \r\nL 175.103842 191.815014 \r\nL 175.19516 199.88115 \r\nL 175.408236 214.756364 \r\nL 175.469115 214.525903 \r\nL 175.499554 214.756364 \r\nL 175.529993 214.232589 \r\nL 175.621312 205.307461 \r\nL 175.71263 214.756364 \r\nL 175.743069 208.869131 \r\nL 175.864827 214.756364 \r\nL 176.017024 194.685301 \r\nL 176.077903 193.993918 \r\nL 176.138782 214.756364 \r\nL 176.260539 214.756364 \r\nL 176.290979 199.147865 \r\nL 176.351857 214.756364 \r\nL 176.443176 209.288151 \r\nL 176.473615 198.226021 \r\nL 176.504054 214.756364 \r\nL 176.534494 209.330053 \r\nL 176.564933 213.101234 \r\nL 176.595373 188.106686 \r\nL 176.625812 214.756364 \r\nL 176.656252 214.735413 \r\nL 176.686691 214.756364 \r\nL 176.71713 204.197057 \r\nL 176.778009 212.870773 \r\nL 176.808449 212.409851 \r\nL 176.838888 214.525903 \r\nL 176.869327 213.01743 \r\nL 176.899767 202.688585 \r\nL 176.930206 214.756364 \r\nL 176.960646 214.756364 \r\nL 177.051964 213.960225 \r\nL 177.082403 214.756364 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214.735413 \r\nL 180.643814 214.756364 \r\nL 180.735132 204.783686 \r\nL 180.85689 214.756364 \r\nL 180.887329 214.756364 \r\nL 180.978647 210.92233 \r\nL 181.100405 179.055852 \r\nL 181.191723 214.756364 \r\nL 181.222163 209.853829 \r\nL 181.252602 214.756364 \r\nL 181.283041 196.466137 \r\nL 181.37436 199.692591 \r\nL 181.465678 195.041468 \r\nL 181.526557 214.756364 \r\nL 181.556996 214.735413 \r\nL 181.587436 200.27922 \r\nL 181.648314 214.756364 \r\nL 181.709193 214.756364 \r\nL 181.739633 204.25991 \r\nL 181.800511 214.756364 \r\nL 181.830951 214.756364 \r\nL 181.86139 158.607672 \r\nL 181.922269 201.9553 \r\nL 181.952708 198.037462 \r\nL 181.983148 208.198699 \r\nL 182.013587 208.911033 \r\nL 182.044027 201.829594 \r\nL 182.074466 214.756364 \r\nL 182.104905 214.756364 \r\nL 182.135345 199.713542 \r\nL 182.196224 207.193051 \r\nL 182.226663 214.756364 \r\nL 182.257103 182.659425 \r\nL 182.317981 210.042388 \r\nL 182.348421 214.756364 \r\nL 182.4093 208.63867 \r\nL 182.439739 210.775673 \r\nL 182.470178 208.408209 \r\nL 182.531057 205.768383 \r\nL 182.622375 214.756364 \r\nL 182.652815 204.155155 \r\nL 182.713694 207.004492 \r\nL 182.744133 213.960225 \r\nL 182.774572 211.718468 \r\nL 182.805012 202.122908 \r\nL 182.835451 214.756364 \r\nL 182.89633 207.528267 \r\nL 183.018088 214.756364 \r\nL 183.109406 214.756364 \r\nL 183.139845 211.299448 \r\nL 183.170285 193.470143 \r\nL 183.200724 213.771666 \r\nL 183.261603 193.574898 \r\nL 183.292042 192.317838 \r\nL 183.322482 214.756364 \r\nL 183.4138 210.964232 \r\nL 183.444239 214.756364 \r\nL 183.535558 188.253343 \r\nL 183.626876 214.756364 \r\nL 183.657315 212.346998 \r\nL 183.687755 214.756364 \r\nL 183.718194 209.036739 \r\nL 183.748633 214.735413 \r\nL 183.809512 207.989189 \r\nL 183.839952 214.756364 \r\nL 183.870391 209.916682 \r\nL 183.992149 214.756364 \r\nL 184.083467 206.857835 \r\nL 184.144346 214.756364 \r\nL 184.174785 211.613713 \r\nL 184.205225 200.551583 \r\nL 184.266103 214.756364 \r\nL 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186.427301 207.758728 \r\nL 186.457741 214.756364 \r\nL 186.48818 212.661263 \r\nL 186.51862 210.733771 \r\nL 186.609938 214.756364 \r\nL 186.640377 168.035624 \r\nL 186.701256 210.461408 \r\nL 186.762135 208.303454 \r\nL 186.792574 195.942362 \r\nL 186.823014 214.756364 \r\nL 186.853453 198.184119 \r\nL 186.975211 214.756364 \r\nL 187.00565 191.668357 \r\nL 187.066529 209.476711 \r\nL 187.096968 214.756364 \r\nL 187.188287 170.486891 \r\nL 187.310044 214.756364 \r\nL 187.340484 214.756364 \r\nL 187.431802 200.928701 \r\nL 187.462241 214.316393 \r\nL 187.492681 199.294522 \r\nL 187.553559 208.84818 \r\nL 187.614438 210.901379 \r\nL 187.644878 194.978615 \r\nL 187.705756 212.80792 \r\nL 187.736196 210.042388 \r\nL 187.857954 183.853632 \r\nL 187.827514 210.92233 \r\nL 187.888393 186.996283 \r\nL 187.949272 214.756364 \r\nL 187.979711 214.735413 \r\nL 188.010151 192.024524 \r\nL 188.04059 214.756364 \r\nL 188.071029 214.756364 \r\nL 188.162348 206.648325 \r\nL 188.192787 164.432051 \r\nL 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188.798069 \r\nL 198.877019 214.756364 \r\nL 198.937898 214.756364 \r\nL 198.998777 194.769105 \r\nL 199.029216 210.817575 \r\nL 199.059656 214.735413 \r\nL 199.090095 186.891528 \r\nL 199.150974 208.911033 \r\nL 199.272731 214.735413 \r\nL 199.303171 210.629016 \r\nL 199.33361 214.756364 \r\nL 199.36405 212.724116 \r\nL 199.394489 179.810088 \r\nL 199.455368 214.756364 \r\nL 199.485807 200.258269 \r\nL 199.577125 214.756364 \r\nL 199.698883 191.794063 \r\nL 199.729322 201.242966 \r\nL 199.790201 191.207435 \r\nL 199.85108 214.756364 \r\nL 199.911959 174.593288 \r\nL 199.972838 201.180113 \r\nL 200.003277 212.367949 \r\nL 200.033717 159.759977 \r\nL 200.064156 214.756364 \r\nL 200.094595 214.756364 \r\nL 200.125035 214.756364 \r\nL 200.155474 212.409851 \r\nL 200.216353 135.792028 \r\nL 200.277232 204.343714 \r\nL 200.36855 214.756364 \r\nL 200.398989 200.48873 \r\nL 200.459868 214.735413 \r\nL 200.490308 214.756364 \r\nL 200.520747 199.441179 \r\nL 200.612065 203.023801 \r\nL 200.703384 214.67256 \r\nL 200.672944 201.368672 \r\nL 200.733823 208.533915 \r\nL 200.764262 205.077 \r\nL 200.794702 214.756364 \r\nL 200.825141 195.104321 \r\nL 200.855581 160.87038 \r\nL 200.88602 214.756364 \r\nL 200.916459 207.423512 \r\nL 200.977338 214.735413 \r\nL 201.038217 177.777841 \r\nL 201.129535 212.17939 \r\nL 201.159975 210.126192 \r\nL 201.251293 214.232589 \r\nL 201.281732 184.545015 \r\nL 201.40349 213.604058 \r\nL 201.464369 208.911033 \r\nL 201.494808 198.393629 \r\nL 201.525248 214.756364 \r\nL 201.555687 214.756364 \r\nL 201.586126 214.421148 \r\nL 201.738323 146.89606 \r\nL 201.829642 214.756364 \r\nL 201.860081 208.63867 \r\nL 201.89052 206.040746 \r\nL 201.92096 212.053684 \r\nL 201.951399 212.493655 \r\nL 201.981839 214.756364 \r\nL 202.012278 214.735413 \r\nL 202.042717 142.140182 \r\nL 202.103596 159.843781 \r\nL 202.164475 214.756364 \r\nL 202.225354 211.844174 \r\nL 202.255793 157.664876 \r\nL 202.286233 214.756364 \r\nL 202.316672 213.85547 \r\nL 202.377551 205.642677 \r\nL 202.40799 214.756364 \r\nL 202.43843 214.484001 \r\nL 202.468869 188.588559 \r\nL 202.499309 214.756364 \r\nL 202.529748 214.484001 \r\nL 202.651506 198.330776 \r\nL 202.681945 214.756364 \r\nL 202.742824 212.849822 \r\nL 202.773263 182.994641 \r\nL 202.834142 190.055129 \r\nL 202.92546 214.756364 \r\nL 202.9559 214.735413 \r\nL 202.986339 170.067871 \r\nL 203.047218 214.756364 \r\nL 203.077657 208.869131 \r\nL 203.168976 211.089938 \r\nL 203.229854 214.337344 \r\nL 203.260294 211.739419 \r\nL 203.321173 211.948929 \r\nL 203.351612 193.449192 \r\nL 203.382051 214.756364 \r\nL 203.47337 202.311467 \r\nL 203.503809 203.547576 \r\nL 203.534248 214.735413 \r\nL 203.564688 165.66816 \r\nL 203.656006 192.715907 \r\nL 203.686445 193.009221 \r\nL 203.716885 214.400197 \r\nL 203.747324 206.627374 \r\nL 203.777764 170.549744 \r\nL 203.808203 214.756364 \r\nL 203.838643 214.756364 \r\nL 203.869082 208.198699 \r\nL 203.929961 209.288151 \r\nL 203.99084 214.756364 \r\nL 204.021279 210.964232 \r\nL 204.082158 176.353172 \r\nL 204.112597 214.756364 \r\nL 204.173476 213.918323 \r\nL 204.203915 214.756364 \r\nL 204.234355 210.482359 \r\nL 204.295234 214.567805 \r\nL 204.356112 211.96988 \r\nL 204.386552 214.756364 \r\nL 204.447431 186.975332 \r\nL 204.47787 211.446105 \r\nL 204.508309 212.870773 \r\nL 204.538749 209.2672 \r\nL 204.569188 207.989189 \r\nL 204.599628 190.159884 \r\nL 204.660507 214.756364 \r\nL 204.690946 214.756364 \r\nL 204.721385 211.907027 \r\nL 204.782264 214.379246 \r\nL 204.812704 192.213083 \r\nL 204.843143 214.756364 \r\nL 204.904022 205.91504 \r\nL 204.934461 205.244608 \r\nL 204.99534 214.756364 \r\nL 205.056219 211.488007 \r\nL 205.086658 213.771666 \r\nL 205.117098 213.352646 \r\nL 205.147537 171.052568 \r\nL 205.208416 207.549218 \r\nL 205.238855 213.394548 \r\nL 205.299734 204.86749 \r\nL 205.360613 214.442099 \r\nL 205.391052 157.74868 \r\nL 205.421492 214.756364 \r\nL 205.451931 214.756364 \r\nL 205.51281 202.688585 \r\nL 205.543249 213.373597 \r\nL 205.604128 211.865125 \r\nL 205.634568 214.756364 \r\nL 205.665007 199.734493 \r\nL 205.725886 214.756364 \r\nL 205.756325 213.310744 \r\nL 205.786765 193.428241 \r\nL 205.847643 214.756364 \r\nL 205.878083 212.849822 \r\nL 205.908522 212.975528 \r\nL 205.969401 188.777118 \r\nL 206.03028 199.650689 \r\nL 206.091159 214.756364 \r\nL 206.152037 205.077 \r\nL 206.212916 214.756364 \r\nL 206.243356 182.76418 \r\nL 206.304235 214.756364 \r\nL 206.425992 191.354092 \r\nL 206.456432 214.756364 \r\nL 206.51731 204.427518 \r\nL 206.54775 198.142217 \r\nL 206.578189 214.756364 \r\nL 206.669507 197.031814 \r\nL 206.760826 214.756364 \r\nL 206.791265 196.256627 \r\nL 206.852144 210.943281 \r\nL 206.882583 214.756364 \r\nL 206.913023 188.588559 \r\nL 207.004341 205.28651 \r\nL 207.03478 214.756364 \r\nL 207.06522 213.373597 \r\nL 207.095659 198.435531 \r\nL 207.156538 205.768383 \r\nL 207.278296 214.756364 \r\nL 207.308735 213.268842 \r\nL 207.339174 214.756364 \r\nL 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175.096112 \r\nL 240.183295 214.735413 \r\nL 240.213735 213.918323 \r\nL 240.244174 175.724642 \r\nL 240.305053 214.756364 \r\nL 240.42681 208.84818 \r\nL 240.45725 209.581466 \r\nL 240.487689 135.540616 \r\nL 240.518129 212.828871 \r\nL 240.548568 211.739419 \r\nL 240.609447 214.756364 \r\nL 240.639886 214.735413 \r\nL 240.670326 181.779483 \r\nL 240.731204 214.756364 \r\nL 240.761644 198.498384 \r\nL 240.792083 214.756364 \r\nL 240.822523 211.194693 \r\nL 240.852962 182.093748 \r\nL 240.883402 214.756364 \r\nL 240.913841 214.735413 \r\nL 240.94428 213.85547 \r\nL 241.035599 214.379246 \r\nL 241.066038 208.512964 \r\nL 241.096477 209.476711 \r\nL 241.157356 214.756364 \r\nL 241.187796 213.478352 \r\nL 241.218235 190.243688 \r\nL 241.279114 214.756364 \r\nL 241.309553 213.771666 \r\nL 241.339993 187.331499 \r\nL 241.400871 214.756364 \r\nL 241.522629 214.756364 \r\nL 241.766144 182.051846 \r\nL 241.887902 214.756364 \r\nL 241.948781 185.005937 \r\nL 241.97922 214.756364 \r\nL 242.00966 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298.687837 214.735413 \r\nL 298.748715 200.572534 \r\nL 298.809594 214.756364 \r\nL 298.870473 206.899737 \r\nL 298.931352 214.756364 \r\nL 298.961791 212.535557 \r\nL 298.992231 202.269565 \r\nL 299.02267 214.756364 \r\nL 299.083549 207.737777 \r\nL 299.235746 214.756364 \r\nL 299.327064 203.903743 \r\nL 299.357503 212.011782 \r\nL 299.387943 214.358295 \r\nL 299.418382 194.769105 \r\nL 299.448822 214.756364 \r\nL 299.479261 214.023078 \r\nL 299.54014 214.504952 \r\nL 299.601019 203.63138 \r\nL 299.722776 214.756364 \r\nL 299.753216 214.756364 \r\nL 299.783655 209.309102 \r\nL 299.844534 210.901379 \r\nL 299.874973 214.106882 \r\nL 299.935852 209.351004 \r\nL 299.966292 212.640312 \r\nL 299.996731 196.864206 \r\nL 300.02717 214.756364 \r\nL 300.05761 207.444463 \r\nL 300.148928 214.756364 \r\nL 300.179367 195.628097 \r\nL 300.270686 201.997202 \r\nL 300.331565 214.756364 \r\nL 300.362004 207.821581 \r\nL 300.392443 190.07608 \r\nL 300.453322 214.756364 \r\nL 300.514201 206.899737 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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": {}
|
|
}
|
|
]
|
|
} |