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569 lines
431 KiB
569 lines
431 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 the wolf. We will train machine learning algorithms that will help Peter to explore the surroinding area and build an optimal navigation map.\n",
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"\n",
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"First, let's import a bunch of userful 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": 1,
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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 cat take some 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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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"from rlboard import *"
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]
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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": 3,
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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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"text/plain": "<Figure size 792x432 with 1 Axes>",
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\n"
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
}
|
|
}
|
|
],
|
|
"source": [
|
|
"width, height = 8,8\n",
|
|
"m = Board(width,height)\n",
|
|
"m.randomize(seed=13)\n",
|
|
"m.plot()"
|
|
]
|
|
},
|
|
{
|
|
"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. To do this, he can essentially walk around until he finds and apple. Therefore, at any position he can chose between one of the following actions: up, down, left and right. We will define those actions as a dictionary, and map them to pairs of corresponding coordinate changes. For example, moving right (`R`) would correspond to a pair `(1,0)`."
|
|
],
|
|
"cell_type": "markdown",
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"actions = { \"U\" : (0,-1), \"D\" : (0,1), \"L\" : (-1,0), \"R\" : (1,0) }\n",
|
|
"action_idx = { a : i for i,a in enumerate(actions.keys()) }"
|
|
]
|
|
},
|
|
{
|
|
"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": {}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "execute_result",
|
|
"data": {
|
|
"text/plain": [
|
|
"18"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"execution_count": 5
|
|
}
|
|
],
|
|
"source": [
|
|
"def random_policy(m):\n",
|
|
" return random.choice(list(actions))\n",
|
|
"\n",
|
|
"def walk(m,policy,start_position=None):\n",
|
|
" n = 0 # number of steps\n",
|
|
" # set initial position\n",
|
|
" if start_position:\n",
|
|
" m.human = start_position \n",
|
|
" else:\n",
|
|
" m.random_start()\n",
|
|
" while True:\n",
|
|
" if m.at() == Board.Cell.apple:\n",
|
|
" return n # success!\n",
|
|
" if m.at() in [Board.Cell.wolf, Board.Cell.water]:\n",
|
|
" return -1 # eaten by wolf or drowned\n",
|
|
" while True:\n",
|
|
" a = actions[policy(m)]\n",
|
|
" new_pos = m.move_pos(m.human,a)\n",
|
|
" if m.is_valid(new_pos) and m.at(new_pos)!=Board.Cell.water:\n",
|
|
" m.move(a) # do the actual move\n",
|
|
" break\n",
|
|
" n+=1\n",
|
|
"\n",
|
|
"walk(m,random_policy)"
|
|
]
|
|
},
|
|
{
|
|
"source": [
|
|
"Let's run random walk experiment several times and see the average number of steps taken:"
|
|
],
|
|
"cell_type": "markdown",
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Average path length = 32.87096774193548, eaten by wolf: 7 times\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def print_statistics(policy):\n",
|
|
" s,w,n = 0,0,0\n",
|
|
" for _ in range(100):\n",
|
|
" z = walk(m,policy)\n",
|
|
" if z<0:\n",
|
|
" w+=1\n",
|
|
" else:\n",
|
|
" s += z\n",
|
|
" n += 1\n",
|
|
" print(f\"Average path length = {s/n}, eaten by wolf: {w} times\")\n",
|
|
"\n",
|
|
"print_statistics(random_policy)"
|
|
]
|
|
},
|
|
{
|
|
"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": 7,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"move_reward = -0.1\n",
|
|
"goal_reward = 10\n",
|
|
"end_reward = -10\n",
|
|
"\n",
|
|
"def reward(m,pos=None):\n",
|
|
" pos = pos or m.human\n",
|
|
" if not m.is_valid(pos):\n",
|
|
" return end_reward\n",
|
|
" x = m.at(pos)\n",
|
|
" if x==Board.Cell.water or x == Board.Cell.wolf:\n",
|
|
" return end_reward\n",
|
|
" if x==Board.Cell.apple:\n",
|
|
" return goal_reward\n",
|
|
" return move_reward"
|
|
]
|
|
},
|
|
{
|
|
"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": 8,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"Q = np.ones((width,height,len(actions)),dtype=np.float)*1.0/len(actions)"
|
|
]
|
|
},
|
|
{
|
|
"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": 9,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": "<Figure size 792x432 with 1 Axes>",
|
|
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"360.646265pt\" version=\"1.1\" viewBox=\"0 0 366.6475 360.646265\" width=\"366.6475pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;white-space:pre;}\n </style>\n </defs>\n <g id=\"figure_1\">\n <g id=\"patch_1\">\n <path d=\"M 0 360.646265 \nL 366.6475 360.646265 \nL 366.6475 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n </g>\n <g id=\"axes_1\">\n <g id=\"patch_2\">\n <path d=\"M 33.2875 336.76814 \nL 359.4475 336.76814 \nL 359.4475 10.60814 \nL 33.2875 10.60814 \nz\n\" style=\"fill:#ffffff;\"/>\n </g>\n <g clip-path=\"url(#p267d475764)\">\n <image height=\"327\" id=\"image00b8757863\" transform=\"scale(1 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\n"
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
}
|
|
}
|
|
],
|
|
"source": [
|
|
"m.plot(Q)"
|
|
]
|
|
},
|
|
{
|
|
"source": [
|
|
"## 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": [
|
|
"def probs(v,eps=1e-4):\n",
|
|
" v = v-v.min()+eps\n",
|
|
" v = v/v.sum()\n",
|
|
" return v"
|
|
]
|
|
},
|
|
{
|
|
"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": 11,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
""
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"\n",
|
|
"from IPython.display import clear_output\n",
|
|
"\n",
|
|
"lpath = []\n",
|
|
"\n",
|
|
"for epoch in range(10000):\n",
|
|
" clear_output(wait=True)\n",
|
|
" print(f\"Epoch = {epoch}\",end='')\n",
|
|
"\n",
|
|
" # Pick initial point\n",
|
|
" m.random_start()\n",
|
|
" \n",
|
|
" # Start travelling\n",
|
|
" n=0\n",
|
|
" cum_reward = 0\n",
|
|
" while True:\n",
|
|
" x,y = m.human\n",
|
|
" v = probs(Q[x,y])\n",
|
|
" a = random.choices(list(actions),weights=v)[0]\n",
|
|
" dpos = actions[a]\n",
|
|
" m.move(dpos,check_correctness=False) # we allow player to move outside the board, which terminates episode\n",
|
|
" r = reward(m)\n",
|
|
" cum_reward += r\n",
|
|
" if r==end_reward or cum_reward < -1000:\n",
|
|
" print(f\" {n} steps\",end='\\r')\n",
|
|
" lpath.append(n)\n",
|
|
" break\n",
|
|
" alpha = np.exp(-n / 3000)\n",
|
|
" gamma = 0.5\n",
|
|
" ai = action_idx[a]\n",
|
|
" Q[x,y,ai] = (1 - alpha) * Q[x,y,ai] + alpha * (r + gamma * Q[x+dpos[0], y+dpos[1]].max())\n",
|
|
" n+=1"
|
|
]
|
|
},
|
|
{
|
|
"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": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": "<Figure size 792x432 with 1 Axes>",
|
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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": [
|
|
"def qpolicy_strict(m):\n",
|
|
" x,y = m.human\n",
|
|
" v = probs(Q[x,y])\n",
|
|
" a = list(actions)[np.argmax(v)]\n",
|
|
" return a\n",
|
|
"\n",
|
|
"walk(m,qpolicy_strict)"
|
|
]
|
|
},
|
|
{
|
|
"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": 14,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Average path length = 3.45, eaten by wolf: 0 times\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"\n",
|
|
"def qpolicy(m):\n",
|
|
" x,y = m.human\n",
|
|
" v = probs(Q[x,y])\n",
|
|
" a = random.choices(list(actions),weights=v)[0]\n",
|
|
" return a\n",
|
|
"\n",
|
|
"print_statistics(qpolicy)"
|
|
]
|
|
},
|
|
{
|
|
"source": [
|
|
"## Investigating the Learning Process"
|
|
],
|
|
"cell_type": "markdown",
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "execute_result",
|
|
"data": {
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|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x7fbab852fd68>]"
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]
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|
},
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|
"metadata": {},
|
|
"execution_count": 15
|
|
},
|
|
{
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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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214.756364 \nL 131.575489 214.756364 \nL 131.666807 205.427301 \nL 131.697247 213.158439 \nL 131.788565 214.756364 \nL 131.910322 203.805877 \nL 131.940762 205.074818 \nL 132.062519 214.756364 \nL 132.184277 208.599652 \nL 132.336474 214.756364 \nL 132.366914 205.568295 \nL 132.427792 210.99654 \nL 132.54955 214.756364 \nL 132.579989 201.972963 \nL 132.640868 212.970447 \nL 132.701747 212.006993 \nL 132.732186 214.756364 \nL 132.762626 209.680602 \nL 132.793065 208.64665 \nL 132.884383 214.756364 \nL 132.914823 210.949542 \nL 132.945262 204.863328 \nL 132.975702 214.756364 \nL 133.006141 214.709366 \nL 133.06702 213.017445 \nL 133.097459 214.756364 \nL 133.158338 214.756364 \nL 133.310535 209.28112 \nL 133.340975 214.756364 \nL 133.401853 208.458659 \nL 133.432293 211.278527 \nL 133.462732 209.633604 \nL 133.55405 207.072224 \nL 133.58449 214.756364 \nL 133.614929 214.756364 \nL 133.645369 201.127003 \nL 133.706247 214.756364 \nL 133.736687 213.440425 \nL 133.797566 202.137456 \nL 133.828005 205.356805 \nL 133.949763 214.756364 \nL 133.980202 214.756364 \nL 134.132399 206.226264 \nL 134.254157 214.756364 \nL 134.284596 214.685867 \nL 134.315036 198.00165 \nL 134.345475 214.756364 \nL 134.375914 199.106098 \nL 134.436793 214.756364 \nL 134.528111 214.497876 \nL 134.558551 214.309885 \nL 134.58899 214.756364 \nL 134.649869 214.685867 \nL 134.680308 213.252434 \nL 134.710748 214.756364 \nL 134.741187 214.756364 \nL 134.802066 212.946949 \nL 134.832506 214.756364 \nL 134.954263 193.184376 \nL 135.076021 214.756364 \nL 135.10646 212.594465 \nL 135.167339 214.756364 \nL 135.289097 214.756364 \nL 135.502172 214.756364 \nL 135.532612 206.766738 \nL 135.593491 214.756364 \nL 135.62393 214.662368 \nL 135.65437 214.756364 \nL 135.745688 195.722257 \nL 135.806567 214.756364 \nL 135.867445 203.923372 \nL 135.989203 214.756364 \nL 136.050082 213.111441 \nL 136.080521 214.756364 \nL 136.110961 214.756364 \nL 136.202279 206.837235 \nL 136.293597 214.756364 \nL 136.324036 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142.594554 214.756364 \nL 142.624994 214.685867 \nL 142.685873 214.756364 \nL 142.716312 214.756364 \nL 142.83807 213.181937 \nL 142.959827 214.756364 \nL 142.990267 214.756364 \nL 143.020706 209.304619 \nL 143.081585 214.474377 \nL 143.203343 212.077489 \nL 143.172903 214.756364 \nL 143.233782 212.805955 \nL 143.385979 214.756364 \nL 143.446858 210.597059 \nL 143.507737 212.453472 \nL 143.538176 214.732865 \nL 143.599055 211.090536 \nL 143.629494 211.325525 \nL 143.690373 214.756364 \nL 143.751252 213.792909 \nL 143.84257 204.81633 \nL 143.964328 214.756364 \nL 144.086085 204.134862 \nL 144.116525 208.270668 \nL 144.207843 214.756364 \nL 144.238282 204.534343 \nL 144.299161 214.756364 \nL 144.329601 214.756364 \nL 144.451358 213.252434 \nL 144.481798 205.121816 \nL 144.512237 214.756364 \nL 144.542677 212.26548 \nL 144.725313 214.756364 \nL 144.755752 214.497876 \nL 144.786192 214.756364 \nL 144.816631 193.583857 \nL 144.907949 204.81633 \nL 144.938389 214.380381 \nL 145.029707 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147.160466 212.970447 \nL 147.221344 214.591871 \nL 147.312663 210.57356 \nL 147.373541 211.231529 \nL 147.403981 214.756364 \nL 147.495299 214.19239 \nL 147.525738 214.732865 \nL 147.556178 208.317666 \nL 147.617057 214.262887 \nL 147.677936 213.816408 \nL 147.799693 214.756364 \nL 147.95189 201.502985 \nL 148.043208 214.756364 \nL 148.073648 211.513516 \nL 148.104087 210.78505 \nL 148.134527 197.79016 \nL 148.164966 214.756364 \nL 148.195405 214.568372 \nL 148.225845 214.756364 \nL 148.347602 211.8425 \nL 148.438921 214.756364 \nL 148.46936 209.093129 \nL 148.530239 212.617964 \nL 148.651997 214.756364 \nL 148.682436 201.549983 \nL 148.743315 214.756364 \nL 148.773754 213.698913 \nL 148.804194 214.756364 \nL 148.834633 202.724928 \nL 148.895512 212.335977 \nL 149.017269 214.756364 \nL 149.047709 214.662368 \nL 149.078148 213.698913 \nL 149.108588 207.213217 \nL 149.169466 214.027898 \nL 149.199906 211.137533 \nL 149.291224 208.787644 \nL 149.321664 214.756364 \nL 149.352103 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151.269786 208.01218 \nL 151.300225 211.889498 \nL 151.330664 190.435005 \nL 151.361104 214.756364 \nL 151.391543 211.748505 \nL 151.421983 212.429973 \nL 151.452422 204.322853 \nL 151.482861 214.756364 \nL 151.513301 207.80069 \nL 151.665498 214.756364 \nL 151.726377 208.975635 \nL 151.756816 210.15058 \nL 151.787256 214.756364 \nL 151.817695 211.748505 \nL 151.848134 206.155767 \nL 151.909013 214.521375 \nL 151.969892 214.756364 \nL 152.000331 214.145392 \nL 152.06121 214.756364 \nL 152.182968 197.625667 \nL 152.243847 214.756364 \nL 152.304725 213.181937 \nL 152.335165 212.71196 \nL 152.365604 214.756364 \nL 152.426483 205.897279 \nL 152.456923 214.756364 \nL 152.548241 208.458659 \nL 152.57868 213.111441 \nL 152.60912 214.756364 \nL 152.700438 214.19239 \nL 152.730877 214.215889 \nL 152.822195 214.756364 \nL 152.852635 208.364663 \nL 152.913514 214.121893 \nL 152.943953 184.654276 \nL 153.065711 214.756364 \nL 153.09615 210.926043 \nL 153.157029 214.756364 \nL 153.187468 214.756364 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205.02782 \nL 154.952954 214.756364 \nL 155.013833 213.534421 \nL 155.044272 206.461253 \nL 155.105151 214.756364 \nL 155.16603 214.756364 \nL 155.196469 204.487345 \nL 155.257348 214.756364 \nL 155.379106 213.228935 \nL 155.439984 211.959995 \nL 155.561742 214.756364 \nL 155.622621 214.756364 \nL 155.713939 205.215811 \nL 155.805257 214.756364 \nL 155.835697 202.865921 \nL 155.896576 212.641463 \nL 156.018333 214.756364 \nL 156.048773 213.322931 \nL 156.109651 214.756364 \nL 156.140091 196.356727 \nL 156.261848 214.756364 \nL 156.322727 207.777191 \nL 156.353167 213.040944 \nL 156.414045 214.756364 \nL 156.566243 204.017367 \nL 156.657561 214.756364 \nL 156.688 214.239388 \nL 156.748879 214.756364 \nL 156.779318 208.035679 \nL 156.840197 207.80069 \nL 156.870637 214.756364 \nL 156.961955 202.912919 \nL 157.022834 214.756364 \nL 157.083712 214.356882 \nL 157.175031 200.539531 \nL 157.23591 214.756364 \nL 157.296788 207.847688 \nL 157.357667 214.756364 \nL 157.388107 204.463846 \nL 157.418546 211.278527 \nL 157.448985 210.103582 \nL 157.479425 213.816408 \nL 157.570743 213.534421 \nL 157.631622 214.756364 \nL 157.692501 207.988681 \nL 157.753379 214.756364 \nL 157.814258 214.521375 \nL 157.844698 214.756364 \nL 157.996895 205.403802 \nL 158.027334 205.521297 \nL 158.149092 214.732865 \nL 158.179531 214.756364 \nL 158.209971 204.510844 \nL 158.270849 211.983494 \nL 158.392607 214.756364 \nL 158.453486 214.756364 \nL 158.483925 212.970447 \nL 158.544804 213.416926 \nL 158.605683 214.756364 \nL 158.666562 210.503063 \nL 158.697001 214.756364 \nL 158.72744 213.816408 \nL 158.788319 214.756364 \nL 158.818759 214.756364 \nL 158.940516 210.832048 \nL 158.970956 211.372522 \nL 159.092713 192.620402 \nL 159.031835 213.76941 \nL 159.123153 200.32804 \nL 159.24491 214.756364 \nL 159.366668 212.194984 \nL 159.397107 212.805955 \nL 159.427547 212.335977 \nL 159.457986 214.756364 \nL 159.518865 212.852953 \nL 159.549304 212.429973 \nL 159.640623 214.756364 \nL 159.671062 214.709366 \nL 159.701502 213.675414 \nL 159.731941 214.756364 \nL 159.76238 214.685867 \nL 159.79282 202.25495 \nL 159.853699 210.855547 \nL 159.975456 214.756364 \nL 160.066774 211.865999 \nL 160.158093 214.756364 \nL 160.27985 211.325525 \nL 160.340729 207.565701 \nL 160.371168 214.756364 \nL 160.492926 200.657025 \nL 160.584244 214.168891 \nL 160.614684 209.28112 \nL 160.736441 214.732865 \nL 160.675563 208.670149 \nL 160.766881 214.568372 \nL 160.858199 214.756364 \nL 160.888638 197.155689 \nL 161.010396 214.756364 \nL 161.071275 214.756364 \nL 161.101714 208.905138 \nL 161.162593 214.756364 \nL 161.284351 211.678008 \nL 161.375669 211.231529 \nL 161.406108 214.756364 \nL 161.527866 209.892092 \nL 161.588745 208.411661 \nL 161.649624 214.756364 \nL 161.740942 213.416926 \nL 161.771381 214.756364 \nL 161.801821 213.440425 \nL 161.83226 207.142721 \nL 161.893139 214.756364 \nL 162.045336 214.756364 \nL 162.167094 208.153173 \nL 162.319291 214.662368 \nL 162.410609 214.756364 \nL 162.441048 205.192312 \nL 162.593245 214.756364 \nL 162.745442 205.591794 \nL 162.775882 214.756364 \nL 162.8672 212.899951 \nL 162.958518 214.756364 \nL 162.928079 212.171485 \nL 162.988958 213.675414 \nL 163.049836 214.756364 \nL 163.080276 213.55792 \nL 163.110715 210.949542 \nL 163.171594 214.756364 \nL 163.202033 214.662368 \nL 163.232473 213.040944 \nL 163.262912 197.696164 \nL 163.323791 214.756364 \nL 163.35423 208.693648 \nL 163.415109 213.910403 \nL 163.445549 214.756364 \nL 163.567306 207.119222 \nL 163.719503 214.756364 \nL 163.749943 214.638869 \nL 163.780382 208.059178 \nL 163.841261 214.756364 \nL 163.8717 212.852953 \nL 163.90214 214.756364 \nL 163.932579 199.670071 \nL 163.993458 209.234123 \nL 164.023897 213.76941 \nL 164.115216 212.476971 \nL 164.145655 214.61537 \nL 164.176094 211.63101 \nL 164.206534 212.735458 \nL 164.236973 212.641463 \nL 164.328291 214.756364 \nL 164.358731 213.510922 \nL 164.38917 214.40388 \nL 164.480489 209.915591 \nL 164.510928 211.725006 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214.239388 \nL 166.428611 214.709366 \nL 166.45905 206.273262 \nL 166.580808 214.756364 \nL 166.611247 212.288979 \nL 166.672126 213.55792 \nL 166.733005 214.756364 \nL 166.885202 209.445613 \nL 167.037399 214.756364 \nL 167.159156 212.500469 \nL 167.220035 214.756364 \nL 167.250475 204.957323 \nL 167.311353 214.756364 \nL 167.433111 212.547467 \nL 167.46355 214.40388 \nL 167.49399 207.80069 \nL 167.585308 207.965182 \nL 167.615747 214.756364 \nL 167.646187 195.22878 \nL 167.707066 214.756364 \nL 167.767945 214.756364 \nL 167.798384 211.865999 \nL 167.859263 214.098395 \nL 167.920142 214.756364 \nL 167.950581 213.299432 \nL 168.01146 214.756364 \nL 168.041899 214.732865 \nL 168.072339 214.333383 \nL 168.163657 193.818846 \nL 168.285414 214.756364 \nL 168.315854 208.787644 \nL 168.376733 211.184531 \nL 168.407172 214.756364 \nL 168.437611 214.450878 \nL 168.468051 203.429895 \nL 168.52893 214.756364 \nL 168.589809 212.100988 \nL 168.620248 212.147986 \nL 168.650687 214.756364 \nL 168.681127 211.513516 \nL 168.742006 213.463924 \nL 168.772445 210.526562 \nL 168.802884 184.325291 \nL 168.863763 214.685867 \nL 168.924642 214.756364 \nL 168.955081 214.027898 \nL 168.985521 209.351617 \nL 169.0464 214.756364 \nL 169.076839 214.756364 \nL 169.107278 207.612699 \nL 169.168157 214.591871 \nL 169.198597 213.628417 \nL 169.229036 214.756364 \nL 169.259475 214.756364 \nL 169.320354 214.027898 \nL 169.442112 200.398537 \nL 169.381233 214.756364 \nL 169.472551 206.132268 \nL 169.56387 214.756364 \nL 169.685627 200.586528 \nL 169.807385 214.756364 \nL 169.868264 214.756364 \nL 169.898703 214.568372 \nL 169.929142 207.824189 \nL 169.959582 214.756364 \nL 169.990021 214.756364 \nL 170.0509 211.396021 \nL 170.081339 214.756364 \nL 170.233537 195.886749 \nL 170.263976 214.756364 \nL 170.355294 213.228935 \nL 170.416173 212.26548 \nL 170.446612 213.76941 \nL 170.477052 213.510922 \nL 170.56837 200.563029 \nL 170.629249 203.782378 \nL 170.751006 214.756364 \nL 170.842325 206.907732 \nL 170.872764 207.824189 \nL 170.994522 214.756364 \nL 171.024961 207.753692 \nL 171.08584 214.662368 \nL 171.116279 214.756364 \nL 171.268476 212.71196 \nL 171.298916 214.638869 \nL 171.329355 210.738052 \nL 171.359795 209.351617 \nL 171.481552 214.709366 \nL 171.511992 214.756364 \nL 171.542431 214.286386 \nL 171.57287 206.884233 \nL 171.60331 214.756364 \nL 171.664189 209.116628 \nL 171.755507 214.756364 \nL 171.785946 214.286386 \nL 171.877265 214.756364 \nL 171.907704 212.124487 \nL 171.938143 214.756364 \nL 171.968583 206.437754 \nL 172.059901 211.396021 \nL 172.09034 213.651915 \nL 172.12078 213.534421 \nL 172.151219 205.756286 \nL 172.181659 214.756364 \nL 172.212098 214.756364 \nL 172.272977 214.756364 \nL 172.303416 213.252434 \nL 172.364295 214.333383 \nL 172.394734 214.756364 \nL 172.486053 208.43516 \nL 172.577371 206.343758 \nL 172.60781 214.756364 \nL 172.63825 191.680446 \nL 172.699129 214.756364 \nL 172.729568 214.333383 \nL 172.760007 214.756364 \nL 172.790447 211.466518 \nL 172.851326 214.756364 \nL 172.912204 214.756364 \nL 172.942644 208.623151 \nL 173.033962 211.772004 \nL 173.12528 214.756364 \nL 173.15572 212.030492 \nL 173.216598 214.756364 \nL 173.338356 214.709366 \nL 173.368796 202.724928 \nL 173.429674 214.756364 \nL 173.460114 214.756364 \nL 173.581871 205.709288 \nL 173.703629 214.756364 \nL 173.734068 214.756364 \nL 173.764508 214.544874 \nL 173.855826 214.662368 \nL 173.977584 214.756364 \nL 174.129781 210.855547 \nL 174.16022 204.134862 \nL 174.19066 214.638869 \nL 174.221099 214.215889 \nL 174.251538 210.620558 \nL 174.281978 214.756364 \nL 174.312417 214.756364 \nL 174.342857 214.756364 \nL 174.464614 204.745833 \nL 174.495054 207.871187 \nL 174.616811 214.756364 \nL 174.647251 214.709366 \nL 174.67769 214.145392 \nL 174.708129 214.709366 \nL 174.769008 203.429895 \nL 174.799448 214.756364 \nL 174.890766 214.756364 \nL 174.982084 213.416926 \nL 175.012524 214.756364 \nL 175.042963 211.560514 \nL 175.073402 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177.112843 214.756364 \nL 177.143282 214.027898 \nL 177.173721 208.270668 \nL 177.2346 208.811143 \nL 177.295479 214.756364 \nL 177.356358 212.241982 \nL 177.417237 214.756364 \nL 177.447676 214.568372 \nL 177.508555 208.106176 \nL 177.538994 214.756364 \nL 177.569434 212.359476 \nL 177.599873 212.335977 \nL 177.660752 214.756364 \nL 177.691191 200.022555 \nL 177.78251 214.756364 \nL 177.812949 213.087942 \nL 177.843388 214.756364 \nL 177.873828 214.638869 \nL 177.904267 196.427223 \nL 177.965146 214.756364 \nL 177.995585 208.599652 \nL 178.056464 209.892092 \nL 178.178222 214.756364 \nL 178.208661 214.756364 \nL 178.29998 208.482158 \nL 178.421737 214.756364 \nL 178.482616 211.443019 \nL 178.513055 214.756364 \nL 178.573934 212.030492 \nL 178.634813 213.158439 \nL 178.665252 214.756364 \nL 178.756571 205.380303 \nL 178.847889 214.756364 \nL 178.878328 207.683195 \nL 178.939207 214.756364 \nL 178.969647 214.756364 \nL 179.030525 210.879046 \nL 179.060965 214.19239 \nL 179.121844 212.993946 \nL 179.182722 210.78505 \nL 179.213162 214.756364 \nL 179.243601 210.432566 \nL 179.274041 202.395943 \nL 179.30448 214.756364 \nL 179.334919 214.756364 \nL 179.365359 214.756364 \nL 179.395798 208.129674 \nL 179.456677 214.215889 \nL 179.487116 214.756364 \nL 179.517556 211.114034 \nL 179.578435 214.756364 \nL 179.608874 214.756364 \nL 179.669753 196.544718 \nL 179.730632 212.05399 \nL 179.791511 214.732865 \nL 179.82195 214.168891 \nL 179.852389 200.821517 \nL 179.913268 214.756364 \nL 180.035026 208.576154 \nL 180.126344 214.756364 \nL 180.156783 214.732865 \nL 180.187223 214.427379 \nL 180.217662 214.756364 \nL 180.278541 203.735381 \nL 180.30898 213.158439 \nL 180.369859 214.756364 \nL 180.400299 214.239388 \nL 180.430738 204.769332 \nL 180.491617 213.933902 \nL 180.552496 214.756364 \nL 180.674253 205.920778 \nL 180.735132 214.756364 \nL 180.765572 211.748505 \nL 180.796011 204.275855 \nL 180.82645 214.756364 \nL 180.85689 211.278527 \nL 180.887329 213.910403 \nL 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204.299354 \nL 187.066529 210.879046 \nL 187.218726 214.756364 \nL 187.340484 211.748505 \nL 187.370923 214.380381 \nL 187.431802 201.808471 \nL 187.462241 214.756364 \nL 187.492681 211.137533 \nL 187.52312 214.756364 \nL 187.553559 209.06963 \nL 187.614438 214.709366 \nL 187.644878 195.369773 \nL 187.736196 196.403725 \nL 187.827514 214.756364 \nL 187.857954 213.675414 \nL 187.888393 214.756364 \nL 188.010151 209.892092 \nL 188.04059 214.544874 \nL 188.101469 187.732631 \nL 188.131908 214.756364 \nL 188.162348 213.017445 \nL 188.192787 202.88942 \nL 188.223226 214.427379 \nL 188.253666 213.158439 \nL 188.344984 214.756364 \nL 188.405863 200.069553 \nL 188.466742 212.359476 \nL 188.52762 214.756364 \nL 188.588499 187.591638 \nL 188.679818 214.756364 \nL 188.710257 214.380381 \nL 188.771136 211.63101 \nL 188.801575 214.286386 \nL 188.832015 214.756364 \nL 188.862454 214.732865 \nL 188.923333 214.756364 \nL 188.984212 202.771926 \nL 189.07553 214.756364 \nL 189.105969 211.278527 \nL 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214.756364 \nL 191.023652 214.356882 \nL 191.054091 201.385491 \nL 191.084531 214.568372 \nL 191.14541 208.64665 \nL 191.267167 214.732865 \nL 191.328046 211.959995 \nL 191.358485 214.756364 \nL 191.388925 214.427379 \nL 191.449804 214.638869 \nL 191.541122 203.594387 \nL 191.571561 213.675414 \nL 191.63244 202.701429 \nL 191.662879 198.283636 \nL 191.784637 214.732865 \nL 191.815077 208.200171 \nL 191.845516 214.756364 \nL 191.906395 210.291573 \nL 191.936834 214.756364 \nL 191.967274 210.174079 \nL 191.997713 199.294089 \nL 192.058592 214.756364 \nL 192.119471 213.205436 \nL 192.14991 214.756364 \nL 192.210789 214.309885 \nL 192.241228 214.756364 \nL 192.271668 203.805877 \nL 192.332546 210.197577 \nL 192.454304 214.756364 \nL 192.606501 208.928637 \nL 192.728259 214.756364 \nL 192.789138 214.286386 \nL 192.819577 201.1975 \nL 192.850016 214.756364 \nL 192.880456 213.651915 \nL 192.941335 211.231529 \nL 192.971774 212.26548 \nL 193.032653 214.756364 \nL 193.15441 190.622996 \nL 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209.774597 \nL 195.467805 208.881639 \nL 195.498245 214.756364 \nL 195.528684 205.944277 \nL 195.589563 214.638869 \nL 195.680881 206.508251 \nL 195.711321 214.756364 \nL 195.802639 211.490017 \nL 195.833078 214.756364 \nL 195.863518 188.837079 \nL 195.924397 214.544874 \nL 196.046154 181.411428 \nL 196.167912 214.756364 \nL 196.289669 200.281043 \nL 196.380988 214.756364 \nL 196.350548 179.696008 \nL 196.411427 213.181937 \nL 196.441866 211.114034 \nL 196.472306 214.756364 \nL 196.502745 212.641463 \nL 196.533185 212.547467 \nL 196.563624 213.76941 \nL 196.594063 211.983494 \nL 196.624503 210.385569 \nL 196.685382 214.756364 \nL 196.746261 213.393428 \nL 196.807139 214.756364 \nL 196.837579 214.568372 \nL 196.898458 214.756364 \nL 196.928897 209.304619 \nL 197.020215 214.756364 \nL 197.050655 212.171485 \nL 197.141973 214.756364 \nL 197.172412 183.526329 \nL 197.29417 214.756364 \nL 197.415928 213.675414 \nL 197.476806 214.756364 \nL 197.507246 214.333383 \nL 197.568125 205.051319 \nL 197.598564 206.555248 \nL 197.629003 214.756364 \nL 197.689882 207.260215 \nL 197.720322 196.803206 \nL 197.750761 214.756364 \nL 197.7812 214.756364 \nL 197.81164 211.302026 \nL 197.872519 214.756364 \nL 197.902958 214.756364 \nL 197.933397 175.842189 \nL 197.994276 213.487423 \nL 198.055155 212.382975 \nL 198.116034 214.756364 \nL 198.176913 187.168658 \nL 198.237792 204.910326 \nL 198.268231 214.756364 \nL 198.32911 206.061771 \nL 198.359549 203.594387 \nL 198.389989 186.111207 \nL 198.450867 214.756364 \nL 198.542186 202.654431 \nL 198.572625 213.55792 \nL 198.603064 213.463924 \nL 198.633504 214.756364 \nL 198.663943 207.542202 \nL 198.724822 214.568372 \nL 198.81614 214.756364 \nL 198.877019 206.320259 \nL 198.907458 214.521375 \nL 198.998777 213.886904 \nL 199.029216 200.516032 \nL 199.090095 201.291495 \nL 199.181413 214.756364 \nL 199.211853 213.087942 \nL 199.242292 214.756364 \nL 199.272731 213.863406 \nL 199.303171 189.753537 \nL 199.394489 205.004321 \nL 199.485807 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205.02782 \nL 204.325673 202.536937 \nL 204.447431 214.756364 \nL 204.47787 214.756364 \nL 204.508309 211.114034 \nL 204.569188 212.664962 \nL 204.660507 214.756364 \nL 204.751825 206.484752 \nL 204.843143 214.756364 \nL 204.873582 213.322931 \nL 204.904022 211.20803 \nL 204.934461 214.756364 \nL 204.964901 183.338337 \nL 205.025779 214.756364 \nL 205.056219 214.521375 \nL 205.117098 214.756364 \nL 205.147537 201.455988 \nL 205.208416 214.756364 \nL 205.360613 214.756364 \nL 205.391052 199.0591 \nL 205.451931 214.756364 \nL 205.482371 213.722412 \nL 205.543249 214.709366 \nL 205.573689 214.756364 \nL 205.665007 207.448206 \nL 205.695446 189.988525 \nL 205.756325 212.617964 \nL 205.786765 214.756364 \nL 205.817204 203.852875 \nL 205.878083 211.443019 \nL 205.938962 214.756364 \nL 205.99984 214.662368 \nL 206.03028 214.756364 \nL 206.152037 191.492455 \nL 206.273795 214.756364 \nL 206.304235 197.625667 \nL 206.365113 214.685867 \nL 206.395553 214.544874 \nL 206.425992 208.411661 \nL 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209.657103 \nL 208.404554 214.756364 \nL 208.434993 210.268074 \nL 208.465432 207.941683 \nL 208.495872 213.416926 \nL 208.556751 214.756364 \nL 208.58719 203.500392 \nL 208.678508 207.354211 \nL 208.708948 206.29676 \nL 208.800266 213.463924 \nL 208.830705 212.429973 \nL 208.861145 203.946871 \nL 208.891584 214.732865 \nL 208.952463 208.317666 \nL 208.982902 213.792909 \nL 209.013342 207.777191 \nL 209.043781 212.899951 \nL 209.135099 214.756364 \nL 209.165539 194.688305 \nL 209.226418 214.756364 \nL 209.287296 212.899951 \nL 209.317736 214.756364 \nL 209.348175 209.586606 \nL 209.409054 213.463924 \nL 209.439493 214.756364 \nL 209.469933 201.573482 \nL 209.530812 213.534421 \nL 209.561251 214.286386 \nL 209.591691 204.064365 \nL 209.652569 209.774597 \nL 209.713448 207.424708 \nL 209.774327 214.756364 \nL 209.804766 206.578747 \nL 209.865645 214.450878 \nL 209.896085 214.756364 \nL 209.987403 208.670149 \nL 210.017842 214.756364 \nL 210.10916 214.215889 \nL 210.1396 208.082677 \nL 210.200479 212.312478 \nL 210.261357 214.756364 \nL 210.291797 213.628417 \nL 210.322236 197.625667 \nL 210.352676 214.756364 \nL 210.383115 214.756364 \nL 210.413555 208.22367 \nL 210.474433 214.544874 \nL 210.504873 214.756364 \nL 210.535312 214.121893 \nL 210.596191 208.85814 \nL 210.62663 210.244575 \nL 210.717949 214.756364 \nL 210.748388 193.066881 \nL 210.809267 214.756364 \nL 210.931024 206.108769 \nL 211.052782 214.756364 \nL 211.113661 214.756364 \nL 211.204979 209.328118 \nL 211.296297 214.756364 \nL 211.326737 209.022633 \nL 211.418055 210.244575 \nL 211.448494 211.701507 \nL 211.509373 213.275933 \nL 211.539813 189.965027 \nL 211.570252 214.756364 \nL 211.66157 201.573482 \nL 211.69201 214.732865 \nL 211.722449 191.915435 \nL 211.752888 211.396021 \nL 211.813767 195.722257 \nL 211.844207 214.756364 \nL 211.874646 214.40388 \nL 211.905086 206.014774 \nL 211.935525 214.756364 \nL 211.965964 214.027898 \nL 211.996404 213.252434 \nL 212.026843 214.756364 \nL 212.057283 198.84761 \nL 212.118161 212.899951 \nL 212.148601 211.701507 \nL 212.17904 199.411583 \nL 212.20948 214.756364 \nL 212.239919 214.333383 \nL 212.300798 214.756364 \nL 212.331237 199.952058 \nL 212.392116 208.85814 \nL 212.422555 211.983494 \nL 212.452995 182.468878 \nL 212.483434 213.158439 \nL 212.513874 203.194906 \nL 212.544313 214.756364 \nL 212.635631 212.735458 \nL 212.666071 206.437754 \nL 212.72695 210.409068 \nL 212.757389 214.756364 \nL 212.818268 213.322931 \nL 212.848707 211.725006 \nL 212.879147 198.236639 \nL 212.909586 214.756364 \nL 212.940025 199.223592 \nL 213.000904 214.756364 \nL 213.061783 212.171485 \nL 213.092222 207.307213 \nL 213.122662 214.756364 \nL 213.153101 210.009586 \nL 213.183541 214.756364 \nL 213.244419 208.341165 \nL 213.274859 214.568372 \nL 213.335738 214.756364 \nL 213.396616 213.510922 \nL 213.427056 214.756364 \nL 213.457495 212.735458 \nL 213.487935 213.9809 \nL 213.518374 209.234123 \nL 213.579253 214.756364 \nL 213.609692 214.756364 \nL 213.761889 197.155689 \nL 213.883647 214.756364 \nL 213.914086 214.756364 \nL 213.944526 214.497876 \nL 214.005405 214.756364 \nL 214.035844 214.756364 \nL 214.066283 214.61537 \nL 214.127162 214.756364 \nL 214.188041 209.422114 \nL 214.309799 214.756364 \nL 214.370678 209.539608 \nL 214.401117 214.662368 \nL 214.431556 214.756364 \nL 214.522875 194.218327 \nL 214.553314 210.244575 \nL 214.614193 209.539608 \nL 214.675072 214.756364 \nL 214.76639 213.275933 \nL 214.857708 214.756364 \nL 214.827269 212.92345 \nL 214.888147 214.450878 \nL 214.918587 204.087864 \nL 215.009905 210.197577 \nL 215.101223 214.756364 \nL 215.131663 214.732865 \nL 215.192542 214.756364 \nL 215.25342 206.484752 \nL 215.28386 212.05399 \nL 215.314299 195.745755 \nL 215.375178 203.006915 \nL 215.496936 214.756364 \nL 215.527375 206.531749 \nL 215.588254 214.756364 \nL 215.618693 214.756364 \nL 215.649133 206.790237 \nL 215.710011 214.732865 \nL 215.77089 214.756364 \nL 215.831769 213.534421 \nL 215.862208 199.90506 \nL 215.923087 208.717147 \nL 216.014406 214.756364 \nL 216.044845 212.92345 \nL 216.105724 202.842423 \nL 216.136163 214.756364 \nL 216.227481 206.978229 \nL 216.257921 214.756364 \nL 216.349239 214.709366 \nL 216.440557 202.372445 \nL 216.410118 214.756364 \nL 216.470997 211.889498 \nL 216.531875 209.868593 \nL 216.592754 214.215889 \nL 216.684072 205.544796 \nL 216.775391 214.756364 \nL 216.80583 206.790237 \nL 216.866709 214.756364 \nL 216.927588 211.396021 \nL 216.958027 186.628183 \nL 216.988467 214.591871 \nL 217.018906 212.758957 \nL 217.049345 209.398615 \nL 217.110224 213.863406 \nL 217.262421 214.756364 \nL 217.292861 201.549983 \nL 217.353739 213.463924 \nL 217.384179 213.675414 \nL 217.414618 200.398537 \nL 217.445058 214.521375 \nL 217.475497 211.560514 \nL 217.505937 214.756364 \nL 217.597255 212.735458 \nL 217.658134 214.756364 \nL 217.719012 202.489939 \nL 217.779891 212.077489 \nL 217.84077 210.832048 \nL 217.932088 214.756364 \nL 217.962528 211.349023 \nL 218.023406 212.876452 \nL 218.114725 214.756364 \nL 218.145164 214.732865 \nL 218.206043 214.756364 \nL 218.297361 200.610027 \nL 218.388679 214.756364 \nL 218.419119 207.095723 \nL 218.540876 214.756364 \nL 218.571316 214.591871 \nL 218.632195 203.077411 \nL 218.662634 211.678008 \nL 218.693073 214.756364 \nL 218.723513 201.385491 \nL 218.784392 211.043538 \nL 218.87571 214.756364 \nL 218.936589 201.878968 \nL 218.967028 214.756364 \nL 218.997467 214.756364 \nL 219.027907 201.737974 \nL 219.088786 214.756364 \nL 219.149665 214.756364 \nL 219.180104 197.696164 \nL 219.240983 214.756364 \nL 219.271422 213.087942 \nL 219.301862 214.450878 \nL 219.332301 195.581263 \nL 219.39318 210.503063 \nL 219.423619 210.080083 \nL 219.454059 212.030492 \nL 219.514937 202.771926 \nL 219.545377 214.756364 \nL 219.575816 212.547467 \nL 219.636695 214.756364 \nL 219.697574 214.756364 \nL 219.819331 213.487423 \nL 219.91065 214.756364 \nL 219.971529 195.722257 \nL 220.001968 214.732865 \nL 220.032407 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222.102287 214.756364 \nL 222.132726 213.228935 \nL 222.193605 214.756364 \nL 222.224045 197.437676 \nL 222.284923 211.889498 \nL 222.345802 210.78505 \nL 222.406681 214.756364 \nL 222.437121 214.497876 \nL 222.46756 212.406474 \nL 222.497999 214.756364 \nL 222.528439 213.722412 \nL 222.650196 214.756364 \nL 222.680636 214.004399 \nL 222.802393 203.147908 \nL 222.832833 206.08527 \nL 222.863272 214.685867 \nL 222.924151 208.64665 \nL 222.95459 206.437754 \nL 223.076348 214.756364 \nL 223.106787 214.732865 \nL 223.137227 213.205436 \nL 223.167666 194.241826 \nL 223.228545 211.278527 \nL 223.289424 210.597059 \nL 223.350303 214.756364 \nL 223.380742 189.236561 \nL 223.47206 204.722334 \nL 223.532939 211.114034 \nL 223.563379 189.941528 \nL 223.593818 214.732865 \nL 223.624257 211.63101 \nL 223.715576 214.756364 \nL 223.746015 203.735381 \nL 223.806894 211.584012 \nL 223.837333 214.756364 \nL 223.867773 206.08527 \nL 223.928652 209.798096 \nL 223.98953 214.756364 \nL 224.01997 197.672665 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228.068411 214.756364 \nL 228.09885 210.291573 \nL 228.159729 214.756364 \nL 228.190169 214.756364 \nL 228.220608 214.380381 \nL 228.251047 199.505579 \nL 228.281487 214.756364 \nL 228.311926 211.560514 \nL 228.342366 212.852953 \nL 228.372805 190.998978 \nL 228.433684 214.521375 \nL 228.464123 214.61537 \nL 228.494563 214.239388 \nL 228.555441 214.756364 \nL 228.61632 203.335899 \nL 228.677199 192.808393 \nL 228.738078 214.756364 \nL 228.890275 207.330712 \nL 228.920714 213.087942 \nL 228.951154 197.437676 \nL 228.981593 214.756364 \nL 229.012033 208.458659 \nL 229.042472 214.756364 \nL 229.13379 213.322931 \nL 229.225108 214.756364 \nL 229.255548 213.440425 \nL 229.285987 214.756364 \nL 229.346866 203.335899 \nL 229.377305 208.43516 \nL 229.468624 214.756364 \nL 229.529502 191.844938 \nL 229.559942 196.192234 \nL 229.6817 214.756364 \nL 229.712139 213.181937 \nL 229.773018 214.732865 \nL 229.864336 213.228935 \nL 229.894775 214.40388 \nL 229.925215 214.732865 \nL 229.955654 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231.72114 210.221076 \nL 231.782019 214.756364 \nL 231.812458 213.76941 \nL 231.903776 200.892014 \nL 231.934216 212.382975 \nL 231.964655 214.756364 \nL 232.055973 213.910403 \nL 232.086413 214.168891 \nL 232.177731 214.239388 \nL 232.20817 196.450722 \nL 232.23861 214.756364 \nL 232.329928 214.286386 \nL 232.360367 214.732865 \nL 232.451686 200.633526 \nL 232.421246 214.756364 \nL 232.482125 208.43516 \nL 232.543004 214.756364 \nL 232.603883 213.745911 \nL 232.664761 213.275933 \nL 232.72564 197.155689 \nL 232.786519 206.132268 \nL 232.877837 214.756364 \nL 232.847398 198.518625 \nL 232.908277 213.252434 \nL 232.999595 214.756364 \nL 233.030034 211.278527 \nL 233.121353 213.275933 \nL 233.24311 200.563029 \nL 233.27355 210.479564 \nL 233.303989 214.756364 \nL 233.395307 212.570966 \nL 233.425747 208.200171 \nL 233.456186 186.581185 \nL 233.517065 211.20803 \nL 233.547504 214.756364 \nL 233.608383 209.140127 \nL 233.638823 207.871187 \nL 233.669262 188.249607 \nL 233.730141 214.756364 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237.839461 199.881561 \nL 237.8699 214.756364 \nL 237.90034 214.685867 \nL 238.052537 203.382897 \nL 238.143855 214.756364 \nL 238.174294 205.615292 \nL 238.235173 211.137533 \nL 238.296052 214.756364 \nL 238.326491 212.547467 \nL 238.356931 198.84761 \nL 238.38737 214.756364 \nL 238.41781 205.967776 \nL 238.539567 214.756364 \nL 238.661325 198.072146 \nL 238.691764 214.756364 \nL 238.783082 212.241982 \nL 238.813522 200.093051 \nL 238.874401 214.756364 \nL 238.90484 203.547389 \nL 239.057037 214.756364 \nL 239.087476 207.213217 \nL 239.148355 211.090536 \nL 239.270113 214.756364 \nL 239.361431 191.539453 \nL 239.42231 214.756364 \nL 239.483189 205.87378 \nL 239.544068 214.756364 \nL 239.604946 210.009586 \nL 239.635386 214.427379 \nL 239.665825 201.385491 \nL 239.696265 214.756364 \nL 239.726704 211.41952 \nL 239.787583 214.450878 \nL 239.818022 209.445613 \nL 239.878901 214.756364 \nL 240.000659 209.375116 \nL 240.031098 191.492455 \nL 240.091977 214.662368 \nL 240.122416 214.61537 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254.733332 214.756364 \nL 254.763771 214.756364 \nL 254.794211 198.730115 \nL 254.885529 206.813736 \nL 254.946408 214.756364 \nL 254.976847 213.487423 \nL 255.007287 141.345807 \nL 255.068165 214.756364 \nL 255.098605 213.886904 \nL 255.159484 196.239232 \nL 255.189923 212.664962 \nL 255.220362 210.808549 \nL 255.250802 212.735458 \nL 255.281241 212.030492 \nL 255.311681 214.662368 \nL 255.34212 201.925966 \nL 255.402999 214.756364 \nL 255.463878 211.513516 \nL 255.494317 199.599575 \nL 255.555196 214.756364 \nL 255.616075 214.756364 \nL 255.646514 213.275933 \nL 255.676954 213.698913 \nL 255.707393 201.033007 \nL 255.737832 214.732865 \nL 255.768272 211.067037 \nL 255.798711 214.145392 \nL 255.829151 194.194828 \nL 255.85959 214.756364 \nL 255.890029 214.756364 \nL 255.920469 214.756364 \nL 255.950908 191.210468 \nL 256.011787 212.71196 \nL 256.042226 208.811143 \nL 256.103105 212.946949 \nL 256.133545 214.756364 \nL 256.163984 214.638869 \nL 256.224863 167.923061 \nL 256.255302 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288.947226 213.064443 \nL 288.977665 214.756364 \nL 289.038544 214.215889 \nL 289.099423 204.111363 \nL 289.129863 208.811143 \nL 289.190741 214.756364 \nL 289.25162 212.876452 \nL 289.28206 214.756364 \nL 289.434257 196.521219 \nL 289.556014 214.756364 \nL 289.586454 212.218483 \nL 289.677772 212.735458 \nL 289.708211 189.04857 \nL 289.76909 212.852953 \nL 289.829969 214.756364 \nL 289.860408 205.051319 \nL 289.951727 211.231529 \nL 289.982166 210.526562 \nL 290.012605 211.043538 \nL 290.043045 212.735458 \nL 290.073484 208.059178 \nL 290.103924 214.732865 \nL 290.134363 212.030492 \nL 290.195242 214.286386 \nL 290.225681 207.213217 \nL 290.28656 214.756364 \nL 290.408318 199.552577 \nL 290.469196 198.283636 \nL 290.530075 214.756364 \nL 290.621394 214.685867 \nL 290.651833 203.523891 \nL 290.712712 214.756364 \nL 290.743151 214.756364 \nL 290.864909 204.557842 \nL 290.925788 214.756364 \nL 291.017106 214.427379 \nL 291.047545 214.356882 \nL 291.077985 190.834486 \nL 291.108424 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297.561578 209.351617 \nL 297.592018 214.756364 \nL 297.622457 201.174001 \nL 297.652897 213.322931 \nL 297.805094 203.899873 \nL 297.896412 214.756364 \nL 297.926851 203.194906 \nL 298.01817 209.962589 \nL 298.139927 214.756364 \nL 298.170367 205.192312 \nL 298.231245 214.756364 \nL 298.261685 214.756364 \nL 298.292124 205.779785 \nL 298.353003 206.696242 \nL 298.383442 214.121893 \nL 298.474761 213.181937 \nL 298.535639 214.756364 \nL 298.566079 211.325525 \nL 298.626958 214.544874 \nL 298.687837 214.756364 \nL 298.748715 213.205436 \nL 298.809594 214.756364 \nL 298.840034 213.886904 \nL 298.870473 203.194906 \nL 298.931352 208.176672 \nL 299.02267 214.756364 \nL 299.053109 208.035679 \nL 299.113988 214.756364 \nL 299.144428 214.662368 \nL 299.235746 207.424708 \nL 299.327064 214.756364 \nL 299.357503 211.772004 \nL 299.387943 211.41952 \nL 299.418382 206.531749 \nL 299.448822 207.612699 \nL 299.479261 214.756364 \nL 299.509701 202.019961 \nL 299.54014 212.641463 \nL 299.601019 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301.366504 207.777191 \nL 301.396944 214.756364 \nL 301.427383 211.090536 \nL 301.457823 202.583935 \nL 301.488262 212.218483 \nL 301.518701 203.923372 \nL 301.640459 214.756364 \nL 301.670898 214.098395 \nL 301.701338 214.756364 \nL 301.731777 196.779707 \nL 301.823095 204.534343 \nL 301.883974 214.756364 \nL 301.914414 211.161032 \nL 301.944853 199.247091 \nL 302.005732 214.732865 \nL 302.036171 209.892092 \nL 302.066611 214.756364 \nL 302.12749 211.137533 \nL 302.157929 210.926043 \nL 302.188368 197.061694 \nL 302.249247 211.748505 \nL 302.279687 208.975635 \nL 302.310126 214.756364 \nL 302.340565 213.910403 \nL 302.401444 214.756364 \nL 302.431884 202.25495 \nL 302.492762 207.918184 \nL 302.553641 214.756364 \nL 302.584081 208.811143 \nL 302.61452 196.004243 \nL 302.644959 214.756364 \nL 302.705838 202.513438 \nL 302.736278 202.536937 \nL 302.888475 214.756364 \nL 303.010232 203.453394 \nL 303.13199 214.756364 \nL 303.192869 206.061771 \nL 303.223308 211.278527 \nL 303.314626 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\n"
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
}
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.plot(lpath)"
|
|
]
|
|
},
|
|
{
|
|
"source": [
|
|
"What we see here is that at first the average path length increased. This is probably due to the fact that when we know nothing about the environment - we are likely to get trapped into bad states, water or wolf. As we learn more and start using this knowledge, we can explore the environment for longer, but we still do not know well where apples are.\n",
|
|
"\n",
|
|
"Once we learn enough, it becomes easier for the agent to achieve the goal, and the path length starts to decrease. However, we are still open to exploration, so we often diverge away from the best path, and explore new options, making the path longer than optimal.\n",
|
|
"\n",
|
|
"What we also observe on this graph, is that at some point the length increased abruptly. This indicates stochastic nature of the process, and that we can at some point \"sploil\" the Q-Table coefficients, by overwriting them with new values. This ideally should be minimized by decreasing learning rate (i.e. towards the end of training we only adjust Q-Table values by a small value).\n",
|
|
"\n",
|
|
"Overall, it is important to remember that the success and quality of the learning process significantly depends on parameters, such as leaning rate, learning rate decay and discount factor. Those are often called **hyperparameters**, to distinguish them from **parameters** which we optimize during training (eg. Q-Table coefficients). The process of finding best hyperparameter values is called **hyperparameter optimization**, and it deserves a separate topic."
|
|
],
|
|
"cell_type": "markdown",
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"source": [
|
|
"## Exercise\n",
|
|
"#### A More Realistic Peter and the Wolf World\n",
|
|
"\n",
|
|
"In our situation, Peter was able to move around almost without getting tired or hungry. In a more realistic world, he has to sit down and rest from time to time, and also to feed himself. Let's make our world more realistic by implementing the following rules:\n",
|
|
"\n",
|
|
"1. By moving from one place to another, Peter loses **energy** and gains some **fatigue**.\n",
|
|
"2. Peter can gain more energy by eating apples.\n",
|
|
"3. Peter can get rid of fatigue by resting under the tree or on the grass (i.e. walking into a board location with a tree or grass - green field)\n",
|
|
"4. Peter needs to find and kill the wolf\n",
|
|
"5. In order to kill the wolf, Peter needs to have certain levels of energy and fatigue, otherwise he loses the battle.\n",
|
|
"\n",
|
|
"Modify the reward function above according to the rules of the game, run the reinforcement learning algorithm to learn the best strategy for winning the game, and compare the results of random walk with your algorithm in terms of number of games won and lost.\n",
|
|
"\n",
|
|
"\n",
|
|
"> **Note**: You may need to adjust hyperparameters to make it work, especially the number of epochs. Because the success of the game (fighting the wolf) is a rare event, you can expect much longer training time.\n",
|
|
"\n"
|
|
],
|
|
"cell_type": "markdown",
|
|
"metadata": {}
|
|
}
|
|
]
|
|
} |