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ML-For-Beginners/8-Reinforcement/1-QLearning/notebook.ipynb

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449 KiB

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"source": [
"# Peter and the Wolf: Reinforcement Learning Primer\n",
"\n",
"In this tutorial, we will learn how to apply Reinforcement learning to a problem of path finding. The setting is inspired by [Peter and the Wolf](https://en.wikipedia.org/wiki/Peter_and_the_Wolf) musical fairy tale by Russian composer [Sergei Prokofiev](https://en.wikipedia.org/wiki/Sergei_Prokofiev). It is a story about young pioneer Peter, who bravely goes out of his house to the forest clearing to chase a wolf. We will train machine learning algorithms that will help Peter to explore the surrounding area and build an optimal navigation map.\n",
"\n",
"First, let's import a bunch of useful libraries:"
],
"cell_type": "markdown",
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},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
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"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import random\n",
"import math"
]
},
{
"source": [
"## Overview of Reinforcement Learning\n",
"\n",
"**Reinforcement Learning** (RL) is a learning technique that allows us to learn an optimal behaviour of an **agent** in some **environment** by running many experiments. An agent in this environment should have some **goal**, defined by a **reward function**.\n",
"\n",
"## The Environment\n",
"\n",
"For simplicity, let's consider Peter's world to be a square board of size `width` x `height`. Each cell in this board can either be:\n",
"* **ground**, on which Peter and other creatures can walk\n",
"* **water**, on which you obviously cannot walk\n",
"* **a tree** or **grass** - a place where you can rest\n",
"* **an apple**, which represents something Peter would be glad to find in order to feed himself\n",
"* **a wolf**, which is dangerous and should be avoided\n",
"\n",
"To work with the environment, we will define a class called `Board`. In order not to clutter this notebook too much, we have moved all code to work with the board into separate `rlboard` module, which we will now import. You may look inside this module to get more details about the internals of the implementation."
],
"cell_type": "code",
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{
"source": [
"Let's now create a random board and see how it looks:"
],
"cell_type": "markdown",
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"execution_count": 3,
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# code block 1"
]
},
{
"source": [
"## Actions and Policy\n",
"\n",
"In our example, Peter's goal would be to find an apple, while avoiding the wolf and other obstacles. 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": [
"# code block 2"
]
},
{
"source": [
"The strategy of our agent (Peter) is defined by a so-called **policy**. A policy is a function that returns the action at any given state. In our case, the state of the problem is represented by the board, including the current position of the player. \n",
"\n",
"The goal of reinforcement learning is to eventually learn a good policy that will allow us to solve the problem efficiently. However, as a baseline, 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. With random walk, we will randomly chose the next action from allowed ones, until we reach the apple. "
],
"cell_type": "markdown",
"metadata": {}
},
{
"source": [
"# Let's run a random walk experiment several times and see the average number of steps taken: code block 3"
],
"cell_type": "code",
"metadata": {},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Average path length = 32.87096774193548, eaten by wolf: 7 times\n"
]
}
],
"source": [
"# code block 4"
]
},
{
"source": [
"## Reward Function\n",
"\n",
"To make our policy more intelligent, we need to understand which moves are \"better\" than others. To do this, we need to define our goal. The goal can be defined in terms of **reward function**, that will return some score value for each state. The higher the number - the better the reward function is.\n",
"\n"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"#code block 5"
]
},
{
"source": [
"An interesting thing about the reward function is that in most of the cases *we are only given substantial reward at the end of the game*. It means that our algorithm should somehow remember \"good\" steps that lead to a positive reward at the end and increase their importance. Similarly, all moves that lead to bad results should be discouraged.\n",
"\n",
"## Q-Learning\n",
"\n",
"An algorithm that we will discuss here is called **Q-Learning**. In this algorithm, the policy is defined by a function (or a data structure) called **Q-Table**. It records the \"goodness\" of each of the actions in a given state, i.e. $Q : {S\\times A}\\to\\mathbb{R}$, where $S$ is a set of states, $A$ is the set of actions.\n",
"\n",
"It is called Q-Table because it is often convenient to represent it as a 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": 55,
"metadata": {},
"outputs": [],
"source": [
"# code block 6"
]
},
{
"source": [
"Notice that we initially initialize all values of Q-Table with equal value, in our case - 0.25. That corresponds to the \"random walk\" policy, because all moves in each state are equally good. We can 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": {
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"m.plot(Q)"
]
},
{
"source": [
"In the center of each cell there is an \"arrow\" that indicates the preferred direction of movement. Since all directions are equal, a dot is displayed.\n",
"\n",
"Now we need to run the simulation, explore our environment, and learn better distribution of Q-Table values, which will allow us to find the path to the apple much faster.\n",
"\n",
"## Essence of Q-Learning: Bellman Equation\n",
"\n",
"Once we start moving, each action will have a corresponding reward, i.e. we can theoretically select the next action based on the highest immediate reward. However, in most of the states the move will not achieve our goal or reaching the apple, and thus we cannot immediately decide which direction is better.\n",
"\n",
"> It is not the immediate result that matters, but rather the final result, which we will obtain at the end of the simulation.\n",
"\n",
"In order to account for this delayed reward, we need to use the principles of **[dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming)**, which allows us to think about our problem recursively.\n",
"\n",
"Suppose we are now at the state $s$, and we want to move to the next state $s'$. By doing so, we will receive the immediate reward $r(s,a)$, defined by reward function, plus some future reward. If we suppose that our Q-Table correctly reflects the \"attractiveness\" of each action, then at state $s'$ we will chose an action $a'$ that corresponds to maximum value of $Q(s',a')$. Thus, the best possible future reward we could get at state $s'$ will be defined as $\\max_{a'}Q(s',a')$ (maximum here is computed over all possible actions $a'$ at state $s'$). \n",
"\n",
"This gives the **Bellman formula** for calculating the value of Q-Table at state $s$, given action $a$:\n",
"\n",
"$$Q(s,a) = r(s,a) + \\gamma \\max_{a'} Q(s',a')$$\n",
"\n",
"Here $\\gamma$ is so-called **discount factor** that determines to which extent you should prefer current reward over the future reward and vice versa.\n",
"\n",
"## Learning Algorithm\n",
"\n",
"Given the equation above, we can now 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",
"In the algorithm above, we did not specify how exactly we should chose an action at step 2.1. If we are choosing the action randomly, we will randomly **explore** the environment, and we are quite likely to die often, and also explore such areas where we would not normally go. An alternative approach would be to **exploit** the Q-Table values that we already know, and thus to chose the best action (with highers Q-Table value) at state $s$. This, however, will prevent us from exploring other states, and quite likely we might not find the optimal solution.\n",
"\n",
"Thus, the best approach is to balance between exploration and exploitation. This can be easily done by choosing the action at state $s$ with probabilities proportional to values in Q-Table. In the beginning, when Q-Table values are all the same, it would correspond to random selection, but as we learn more about our environment, we would be more likely to follow the optimal route, however, choosing the unexplored path once in a while.\n",
"\n",
"## Python Implementation\n",
"\n",
"Now we are ready to implement the learning algorithm. Before that, we also need some function that will convert arbitrary numbers in the Q-Table into a vector of probabilities for corresponding actions:"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# code block 7"
]
},
{
"source": [
"We add small amount `eps` to the original vector in order to avoid division by 0 in the initial case, when all components of the vector are identical.\n",
"\n",
"The actual learning algorithm we will run for 5000 experiments, also called **epochs**: "
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
""
]
}
],
"source": [
"\n",
"from IPython.display import clear_output\n",
"\n",
"lpath = []\n",
"\n",
"# code block 8"
]
},
{
"source": [
"After executing this algorithm, the Q-Table should be updated with values that define the attractiveness of different actions at each step. We can try to visualize the Q-Table by plotting a vector at each cell that will point in the desired direction of movement. For simplicity, we draw a small circle instead of arrow head."
],
"cell_type": "code",
"metadata": {},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"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. This happens because there could be situations when two states \"point\" to each other in terms of optimal Q-Value, in which case the agents ends up moving between those states indefinitely.\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.\n",
"\n",
"Better navigation policy would be the one that we have used during training, which combines exploitation and exploration. In this policy, we will select each action with a certain probability, proportional to the values in Q-Table. This strategy may still result in the agent returning back to the position it has already explored, but, as you can see from the code below, it results in very short average path to the desired location (remember that `print_statistics` runs the simulation 100 times): "
],
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"Average path length = 5.31, eaten by wolf: 0 times\n"
]
}
],
"source": [
"\n",
"# code block 10"
]
},
{
"source": [
"## Investigating Learning Process\n",
"\n",
"As we have mentioned, the learning process is a balance between exploration and exploration of gained knowledge about the structure of problem space. We have seen that the result of learning (the ability to help an agent to find short path to the goal) has improved, but it is also interesting to observe how the average path length behaves during the learning process: "
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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 134.041081 200.949652 \r\nL 134.07152 214.525903 \r\nL 134.10196 203.652331 \r\nL 134.193278 203.128556 \r\nL 134.223717 214.756364 \r\nL 134.345475 198.603139 \r\nL 134.406354 214.756364 \r\nL 134.436793 177.191213 \r\nL 134.497672 211.886076 \r\nL 134.528111 213.876421 \r\nL 134.61943 212.766018 \r\nL 134.680308 214.756364 \r\nL 134.710748 189.02853 \r\nL 134.771627 214.756364 \r\nL 134.802066 214.693511 \r\nL 134.862945 214.756364 \r\nL 134.893384 197.807001 \r\nL 134.954263 214.756364 \r\nL 134.984703 214.735413 \r\nL 135.015142 200.090661 \r\nL 135.076021 212.766018 \r\nL 135.10646 214.756364 \r\nL 135.1369 211.76037 \r\nL 135.167339 206.878786 \r\nL 135.197778 214.756364 \r\nL 135.228218 214.756364 \r\nL 135.258657 170.277381 \r\nL 135.319536 214.358295 \r\nL 135.380415 214.756364 \r\nL 135.441294 214.714462 \r\nL 135.532612 214.735413 \r\nL 135.593491 177.673086 \r\nL 135.684809 214.756364 \r\nL 135.715248 214.735413 \r\nL 135.776127 200.802995 \r\nL 135.806567 214.756364 \r\nL 135.837006 214.735413 \r\nL 135.867445 200.006856 \r\nL 135.928324 204.804637 \r\nL 136.050082 214.756364 \r\nL 136.080521 197.57654 \r\nL 136.1414 202.018153 \r\nL 136.202279 214.756364 \r\nL 136.232718 213.43645 \r\nL 136.293597 214.756364 \r\nL 136.354476 190.956023 \r\nL 136.384915 214.756364 \r\nL 136.476234 213.64596 \r\nL 136.537112 212.284145 \r\nL 136.567552 214.756364 \r\nL 136.597991 209.895731 \r\nL 136.689309 210.356653 \r\nL 136.719749 214.735413 \r\nL 136.811067 212.849822 \r\nL 136.902385 214.756364 \r\nL 136.963264 207.633022 \r\nL 137.024143 211.823223 \r\nL 137.054582 214.735413 \r\nL 137.085022 208.240601 \r\nL 137.115461 214.484001 \r\nL 137.17634 214.756364 \r\nL 137.267658 187.289597 \r\nL 137.389416 214.756364 \r\nL 137.419855 189.02853 \r\nL 137.480734 189.803717 \r\nL 137.572052 214.756364 \r\nL 137.602492 208.827229 \r\nL 137.632931 207.486365 \r\nL 137.754689 214.756364 \r\nL 137.785128 212.3889 \r\nL 137.815567 198.561237 \r\nL 137.876446 214.756364 \r\nL 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205.600775 \r\nL 146.977829 209.937633 \r\nL 147.008269 172.079168 \r\nL 147.038708 214.756364 \r\nL 147.069147 206.501668 \r\nL 147.130026 203.882792 \r\nL 147.190905 214.756364 \r\nL 147.221344 214.421148 \r\nL 147.251784 201.9553 \r\nL 147.312663 212.577459 \r\nL 147.373541 214.756364 \r\nL 147.43442 206.857835 \r\nL 147.46486 188.064784 \r\nL 147.495299 213.01743 \r\nL 147.525738 211.634664 \r\nL 147.556178 200.970603 \r\nL 147.586617 214.756364 \r\nL 147.617057 207.821581 \r\nL 147.677936 214.756364 \r\nL 147.738814 214.735413 \r\nL 147.769254 210.587114 \r\nL 147.830133 211.173742 \r\nL 147.921451 214.756364 \r\nL 147.95189 214.735413 \r\nL 148.043208 179.956745 \r\nL 148.164966 214.756364 \r\nL 148.195405 213.43645 \r\nL 148.256284 214.756364 \r\nL 148.286724 187.645764 \r\nL 148.408481 214.756364 \r\nL 148.4998 209.183396 \r\nL 148.530239 210.880428 \r\nL 148.560678 214.651609 \r\nL 148.591118 199.294522 \r\nL 148.651997 214.735413 \r\nL 148.712875 214.756364 \r\nL 148.743315 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152.791756 194.685301 \r\nL 152.822195 214.756364 \r\nL 152.913514 214.735413 \r\nL 152.943953 214.756364 \r\nL 152.974392 193.470143 \r\nL 153.035271 214.735413 \r\nL 153.09615 213.038381 \r\nL 153.126589 213.771666 \r\nL 153.157029 214.756364 \r\nL 153.187468 214.735413 \r\nL 153.278787 212.17939 \r\nL 153.370105 214.756364 \r\nL 153.491862 210.000486 \r\nL 153.522302 214.106882 \r\nL 153.552741 212.996479 \r\nL 153.583181 180.208157 \r\nL 153.644059 186.807724 \r\nL 153.704938 209.811927 \r\nL 153.765817 197.031814 \r\nL 153.857135 214.148785 \r\nL 153.887575 203.400919 \r\nL 154.039772 214.756364 \r\nL 154.161529 209.309102 \r\nL 154.222408 214.756364 \r\nL 154.283287 195.565244 \r\nL 154.313726 210.901379 \r\nL 154.374605 208.994837 \r\nL 154.465923 214.756364 \r\nL 154.61812 153.495627 \r\nL 154.678999 214.756364 \r\nL 154.739878 214.714462 \r\nL 154.770317 214.735413 \r\nL 154.831196 214.756364 \r\nL 154.861636 198.959306 \r\nL 154.952954 214.756364 \r\nL 155.074712 200.823946 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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 184.296543 214.756364 \r\nL 184.387861 203.191409 \r\nL 184.509619 214.756364 \r\nL 184.540058 208.994837 \r\nL 184.600937 214.756364 \r\nL 184.631376 214.756364 \r\nL 184.661816 195.523342 \r\nL 184.722695 214.756364 \r\nL 184.783573 214.756364 \r\nL 184.93577 200.404926 \r\nL 184.96621 214.735413 \r\nL 185.057528 213.541205 \r\nL 185.118407 214.044029 \r\nL 185.240164 192.275936 \r\nL 185.331483 187.373401 \r\nL 185.361922 214.756364 \r\nL 185.392362 203.882792 \r\nL 185.45324 213.981176 \r\nL 185.48368 214.756364 \r\nL 185.544559 180.103402 \r\nL 185.574998 214.756364 \r\nL 185.605437 214.756364 \r\nL 185.757634 190.599855 \r\nL 185.788074 192.171181 \r\nL 185.818513 181.695679 \r\nL 185.909831 214.756364 \r\nL 185.940271 203.149507 \r\nL 185.97071 214.756364 \r\nL 186.031589 202.16481 \r\nL 186.062028 213.22694 \r\nL 186.092468 195.271929 \r\nL 186.153347 207.130198 \r\nL 186.214226 214.756364 \r\nL 186.244665 207.402561 \r\nL 186.305544 213.981176 \r\nL 186.396862 211.236595 \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 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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 207.369614 198.498384 \r\nL 207.430493 211.048036 \r\nL 207.521811 214.609707 \r\nL 207.58269 214.756364 \r\nL 207.613129 199.126914 \r\nL 207.704447 214.756364 \r\nL 207.734887 214.442099 \r\nL 207.765326 208.806278 \r\nL 207.795765 214.735413 \r\nL 207.826205 214.232589 \r\nL 207.856644 214.756364 \r\nL 207.887084 200.509681 \r\nL 207.947963 214.46305 \r\nL 208.008841 214.756364 \r\nL 208.06972 210.314751 \r\nL 208.10016 176.164613 \r\nL 208.130599 212.493655 \r\nL 208.161038 212.200341 \r\nL 208.221917 195.271929 \r\nL 208.252357 213.394548 \r\nL 208.282796 214.756364 \r\nL 208.313235 214.735413 \r\nL 208.343675 204.280861 \r\nL 208.374114 214.756364 \r\nL 208.404554 214.756364 \r\nL 208.465432 214.756364 \r\nL 208.495872 209.623368 \r\nL 208.526311 159.257153 \r\nL 208.556751 214.756364 \r\nL 208.617629 180.0615 \r\nL 208.648069 214.735413 \r\nL 208.739387 213.583107 \r\nL 208.769827 214.756364 \r\nL 208.800266 191.584553 \r\nL 208.861145 210.105241 \r\nL 208.891584 206.75308 \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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196.989912 \r\nL 276.284433 214.46305 \r\nL 276.314872 214.714462 \r\nL 276.375751 214.756364 \r\nL 276.43663 213.038381 \r\nL 276.467069 214.756364 \r\nL 276.497508 204.825588 \r\nL 276.588827 206.878786 \r\nL 276.619266 204.888441 \r\nL 276.649705 213.750715 \r\nL 276.741024 210.230947 \r\nL 276.801902 206.250256 \r\nL 276.832342 214.756364 \r\nL 276.862781 205.789334 \r\nL 276.92366 214.67256 \r\nL 277.014978 205.056049 \r\nL 277.075857 214.756364 \r\nL 277.106297 200.27922 \r\nL 277.136736 191.437896 \r\nL 277.167175 214.756364 \r\nL 277.228054 203.882792 \r\nL 277.258494 214.756364 \r\nL 277.349812 214.756364 \r\nL 277.380251 206.187403 \r\nL 277.44113 209.644319 \r\nL 277.471569 214.756364 \r\nL 277.532448 213.666911 \r\nL 277.562888 199.67164 \r\nL 277.623766 214.756364 \r\nL 277.684645 214.756364 \r\nL 277.775964 204.0504 \r\nL 277.867282 214.756364 \r\nL 277.9586 196.151872 \r\nL 277.989039 214.756364 \r\nL 278.080358 214.085931 \r\nL 278.141236 191.898818 \r\nL 278.171676 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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": [
"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",
"#### 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 more realistic world, we 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": {}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
]
}