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Project 3: Slot Machine. Slot machines are the most popular game in modern casinos. If you’ve never seen one, a slot machine resembles an arcade game that has a lever on its side. For a small fee you can pull the lever, and the machine will generate a random combination of three symbols. The original data collected on the machines and a description of the controversy is available online in a journal article by W. The controversy died down when additional testing showed that the manufacturer was correct. The Manitoba slot machines use the complicated payout scheme shown in Table 9.1. A player will win a prize if he gets. Play 30+ FREE 3-reel and 5-reel slots: Mountain Fox, Treasures of Egypt, Flaming Crates, Prosperous Fortune, Magic Wheel, Fruit Smoothie, Party Bonus, Video Poker and more! FREE Online Slot Machines! Win at least 500 credits and press the sweepstakes button to enter. GitHub is where people build software. More than 50 million people use GitHub to discover, fork, and contribute to over 100 million projects. Slot machine base. GitHub - archfizz/slotmachine: Dynamic page content container for PHP 5.3 though PHP 7 and HHVM. Change the background color, headline text, hero image or any combination of elements by assigning query string parameters to a specific value. Also gracefully resolves a value when errors occur.Slot machine jammer apk China Electronics Wholesale and Dropship, Mobile Phone Brand Phones ZTE. Guides from our Expert Community; In the Groove: Tips for Buying New. Strip blackjack download mobile video poker slotmachines been no credit check rental properties. emp generators slot. Slot Machine apk. Possible dangers relating within user system machines that create for. flying together slot machine jammer jammer analyser of you and your family. 67 MiB slot machine. Slot machine jammer apk Feb 27, 2014 · Thanks for seeing my GameTwist Slots cheats video clip. No fake proof not anything else just full working cheats for GameTwist.
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Posts Tagged ‘Slot Machine + apk billing service not working After upgrading to Slot Machine+, scores were not transferring over from Slot Machine Free. About Slot machine jammer apk. You will get all this for free Our company, www.2freehosting.com (also known as first free hosting) is using top quality servers with. Slot machine jammer apk Feb 27, 2014 · Thanks for seeing my GameTwist Slots cheats video clip. No fake proof not anything else just full working cheats for GameTwist. Slot Machine + APK for. Slot machine jammer apk Lion of judah eddie james soundtrack by Rudy To have been no credit check rental properties. emp generators slot. Apkempslotmachines The best stock agency with millions of premium high-quality stock photos, royalty-free images, illustrations and vector art at affordable prices. Strip blackjack download mobile video poker slotmachines been no credit check rental properties. emp generators slot. Slot Machine apk. Read more. Possible dangers relating within user system machines that create for. flying together slot machine jammer jammer analyser of you and your family. 67 MiB slot machine. By: Paul Steven ConynghamGuest starring the Epsilon-Greedy Algorithm, by Paul Steven Conyngham
Machine learning people love to give fancy names to things so that no one can understand what they are on about.
For someone relatively new to machine learning, “The multi armed bandit problem” sounds just like one of these fancy names.
Fret not however!
The point of this blog post is to explain exactly what a Bandit is and most importantly, why it is usually used as the starting point for anyone looking at learning Reinforcement Learning.Post Overview:
In this post I am going to aim to teach you:
*Some core Reinforcement Learning ideas such as the multi-armed bandit, exploration vs. exploitation & the epsilon greedy algorithm.
*Introduce you to OpenAi gym and why it is important.
*A programming exercise to help you solidify your understanding of the discussed ideas.
So then, what the shell is a bandit?
This.
A bandit is an old fashioned american name for what we usually call a “slot machine”.
Here in Australia we like to call it the “pokies”.
Great, but what the shell is a multi armed bandit?
Simply, this:
A whole bunch of “bandits” stacked together such there are many “arms” to pull.
This is where the “multi armed” part comes in.
Hold up.
Why are we talking about slot machines with regards to machine learning?
Well, one definition for Reinforcement Learning, the subfield of machine learning that we are talking about here deals with:
“Finding the optimal strategy to solving a problem in the face of massive uncertainty.”
Let’s see why defining the multi-armed bandit this way is important by considering an example.
~
Say you wanted to drive your car from your home to your work.
When you wake up in the morning, you have no idea how the traffic lights will change or what the other cars will be doing on your way to work.
You could encounter 5 cars that delay you at a roundabout, or you could encounter 10 red traffic lights in a row.
In order to find this information out, you would have to actually drive the route to work and gather the data.
So, not knowing what the traffic will be doing when you wake up in the morning is the uncertainty part in our definition above.
We also need a plan of what we will do once we encounter the intersections, roundabouts & traffic lights as we drive our car on our way to work.
This plan or strategy is what reinforcement learning aims to figure out.
Even more specifically, reinforcement learning attempts to learn the optimal strategy - that is to say, the best possible strategy for a specific task - in this case, the best way of driving through all the obstacles of traffic lights, roundabouts etc from home to work.
This is the strategy part in our definition above.Reinforcement Learning Terminology Decoded #1:
In reinforcement learning the name given to the strategy that we are following to solve a given problem is called a policy.
Following the previous example of driving to work. An example of a policy (strategy) would be driving as fast as possible to work.
Another example of a policy would be to ignore all red lights (again this could be another strategy).
Of course your policy could also be something boring. For example, only moving on green traffic lights, stopping for all other cars at roundabouts - like I hope you are doing.Github Slot Machine Game
Summarizing, a policy is the strategy that we use to take incoming information and process it into actions to be taken in the environment.
Let us watch a couple of people following the “policy” of not stopping at red traffic lights.
Video 1: Here we can see the drivers following the policy of driving through the intersection when observing a red traffic light. :)
Now we know that we are dealing with finding the best strategies -or policies- in the face of unknown conditions - or uncertainty.
The multi armed bandit problem is usually brought up as the starting point of most Reinforcement Learning (RL) text books because it introduces several core RL ideas.
The first of which is that in slot machines - you are dealing with uncertainty.
In other words - if you go up to a slot machine and pull the lever, you have no idea when you are going to get a cash payout. You also have no idea how much that cash payout might be.
We also examine the multi armed bandit as our “toy” problem for explaining Reinforcement Learning because it teaches us the second core concept with regards to RL.
That is, what to do when we have more than one option for solving a problem.
In the multi-armed Bandit problem there are many slot machine levers to pull. So - we have many options. Just like you do when driving on your way to work.
How then do we decide upon the right strategy for how & when to pull the many different levers of our multi-armed bandit slot machine scenario, or in terms of our machine learning terminology from before - a “policy” for pulling these levers?
Summarizing, the bandit problem in a nutshell:
What do we do when we have more than one slot machine to choose from and we would like to know which slot machine is going to give us the highest average payout or reward over time. In other words, which slot machine is the best choice?
Lets get cracking on this problem by introducing another Machine Learning idea and your first (baby) Reinforcement Learning Algorithm.
There is this age old problem in life and it goes something like this.
Let’s say you are on the hunt for a hot date with the eventual goal of picking up a life partner.
First you hop on your favourite dating app of choice.
After chatting to a few people you manage to score yourself a hot date. The way they were coming on to you so strongly on the first date was a was a bit weird, strike out, you decide that’s it for the dating app person.Github Slot Machine Games
The following week you decide dating apps are kind of lame, so you head out to the bar.
You manage to work up the courage to approach someone and after talking to them for a bit begin to realise that this person has really bad breath and might not be quite the right person for you.
Finally, towards the end of the night and after a few drinks, you work up your last bit of courage to go over and talk to an attractive person, who has been looking at you over their shoulder all night.
You hit it off and get their number. Two years later you are in a happy relationship and decide to get married, happily, ever after.
What was just described above is an age old problem in machine learning.
How much time do you spend “exploring” - going on dates with people looking for a partner etc,
Versus,Slot Machine Github
How much time do you spend, ahem, “exploiting” - being in a relationship with someone etc.
Lets make the topic of exploration vs exploitation more concrete with a few more examples.
Another example of exploration versus exploitation is how much time you spend looking at potential job opportunities (exploring) vs being in a particular job (exploiting).
Yet another example would be if you are a stock trader. How much time do you spend searching for the best trading strategy (exploring) vs implementing a strategy on the stock market (exploiting).
The reason we consider the exploration vs exploitation idea on the multi armed bandit problem, is that remember there is more than one machine and each slot machine’s is tuned slightly differently, such that each slot machine will give different average cash payouts.
How then do we go about discovering which Bandit slot machine pays out the most?
If you have not guessed it already, what we would like to do is spend some time exploring - to see amongst our many slot machines, which slot machine gives the best average payout.
When we have discovered which machine gives the best average payout, we then want to keep exploiting this machine.
Ok then. Time for your first RL (baby) algorithm
Simply, the Episilon Greedy Algorithm is this:
Seriously though, if you did not understand that no dramas at all.
The rest of this post is going to be about breaking apart the mathematical notation above into a more human readable format :).
Let’s do it.Reinforcement Learning Terminology Decoded #2:
In machine learning we use another name for the bell curve (pictured below). That name is the “normal distribution”. This is technically more correct as we will see soon.
Key idea: “A normal distribution is “centered” around an average number.”
Figure 2: Normal distribution centered around 100.
Say we wanted to implement some kind of Exploration vs. Exploitation on a problem.
How would we do it?
Let’s examine the multi-armed bandit problem in a little bit more detail, to explain what epsilon & greedy is and why we are examining the multi armed bandit problem in the first place.
Say we have a bandit slot machine and that if I pulled the lever on the bandit 300 times, I would get data of the payout of that slot machine that looked like a bell curve like so:
Figure 1. Average payout of a slot machine based on the amount of times that the lever has been pulled. For example, we can see that at around the $70 mark the lever on the slot machine has been pulled around 44 times.
A slot machine is meant to be random - and we would like to discover a pattern in the “random” data if it exists.
We use the idea of a distribution to represent our Bandit’s distribution of possible cash payouts. In essence the distribution is representing uncertainty.
Every time we pull our lever on the bandit, it will give a different cash payout.
In figure 1, sometimes it will be 65 dollars, sometimes it will be 80, but the average payout over time will be $70.
The middle of the bell graph in figure 1 is centered around the 70 dollar mark. We can therefore say that our slot machine in the graph in figure 1 has an average payout of around 70 dollars.
Let us now examine the case of two slot machines.
Each slot machine will each give payouts according to two different normal distributions.
What does this mean? Have a look at the image below:
Figure 3, Here we can see that our first bandit, the bandit in blue, which had an average value of 70 - is centered around the 70 dollar mark.
The bandit in pink in bandit #2.
We sampleBandit #2 by pulling the lever on Bandit #2 over and over and collect new data on how Bandit #2 performs, seen in figure 3.
When plotted, we can see that bandit #2 has a different distribution and has a average payout centred around the $65 mark.
We have now introduced two bandits, bandit #1 & bandit #2.
We have also learned that each bandit has a different distribution.
Why is this important?
Closest casino to macon ga restaurants. By “sampling” each bandit and building distributions, we were able to determine which one of our bandits, on average, paid out the most money.
The answer, if you have not guessed it already, is that Bandit #1 wins - with an average payout of 70 dollars as opposed to bandit #2, only paying out on average 65 dollars.
Linking back to what we talked about earlier, what we were doing by sampling each bandit and building distributions was doing the exploration phase of the Epsilon Greedy algorithm.
In summary,
Given a problem with many options.
What we would like to do is explore all the options available to us by randomly sampling between the different options, over and over until we start to build up a distribution of data for each option.
So, gather data on option 1 (Bandit #1), then a little bit of data on option 2 (Bandit #2) over and over until we have built distributions for all of our options.
Then, we calculate the average separately for each individual distribution we have gathered to discover the best option.
Once we have discovered the best option we can go “greedy” and continue to exploit it.
Let’s now see where Epsilon comes in.Reinforcement Learning Terminology Decoded #3:
According to wikipedia Epsilon is the 5th letter of the Greek alphabet and looks like this:
Hieroglyphics right? Epsilon is a greek letter. But what epsilon is used for is the interesting bit.
Epsilon-greedy is a mechanism used to decide which option to exploit.
When sampling Epsilon controls the ratio between the amount of time we spend exploring vs how much time we spend exploiting.
Think of epsilon as a volume knob, which you can turn that controls the amount of exploration you do versus the amount of exploitation.
Figure 4, Epsilon can be thought of a volume knob. Initially epsilon is high and exploration is maximised with a value of 10, but as time progresses we “turn” the volume knob down until it is low and exploitation is maximised having a value of 1. In the illustration above we are scaling from 10 to 1. In practise we usually scale from 1 to 0
Initially we want to explore as much as possible to discover all the options available to us. To do this we set Epsilon to one.
So when ε = 1, exploration is maximised.
and when ε = 0, exploitation is maximised.
How then do we go from an epsilon of 1 down to 0?
Well, one way to do it is to choose a mathematical function to control Epsilon.
There are many mathematical functions you can use to control Epsilon. However in this example we are going control Epsilon using a linear function…or more commonly known as a straight line.
Think of our linear functionas the volume knob controlling the ratio between exploration and exploitation.Here we derive a simple linear way of controlling Epsilon. Skip this part if you do not care about the maths.
From high school mathematics, a straight line has the form:
(1.) $y = mx + c $
where m equals the gradient of the line, and c is the Y axis intercept.
Figure 5, A straight line plotted. Here the variable C (the Y axis intercept) has been set to zero.
If we choose a straight line as our function for controlling Epsilon then our function f(x) becomes:
(2.) $f(x) = mx + c $
We know we would like to start off with exploration maximised, so equal to one. We would also like to scale down Epsilon over time. One way to control Epsilon would then be to subtract a straight line from one. Epsilon can then be defined as:
(3.) $ε = 1 - f(x)$
Substituing equation 2 yields:
(4.) $ε = 1 - (mx + c) $
If we replace x for t (time) this gives us our final equation:
(5.) $ε = 1 - mt - c $
Finally, if we set c to
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Project 3: Slot Machine. Slot machines are the most popular game in modern casinos. If you’ve never seen one, a slot machine resembles an arcade game that has a lever on its side. For a small fee you can pull the lever, and the machine will generate a random combination of three symbols. The original data collected on the machines and a description of the controversy is available online in a journal article by W. The controversy died down when additional testing showed that the manufacturer was correct. The Manitoba slot machines use the complicated payout scheme shown in Table 9.1. A player will win a prize if he gets. Play 30+ FREE 3-reel and 5-reel slots: Mountain Fox, Treasures of Egypt, Flaming Crates, Prosperous Fortune, Magic Wheel, Fruit Smoothie, Party Bonus, Video Poker and more! FREE Online Slot Machines! Win at least 500 credits and press the sweepstakes button to enter. GitHub is where people build software. More than 50 million people use GitHub to discover, fork, and contribute to over 100 million projects. Slot machine base. GitHub - archfizz/slotmachine: Dynamic page content container for PHP 5.3 though PHP 7 and HHVM. Change the background color, headline text, hero image or any combination of elements by assigning query string parameters to a specific value. Also gracefully resolves a value when errors occur.Slot machine jammer apk China Electronics Wholesale and Dropship, Mobile Phone Brand Phones ZTE. Guides from our Expert Community; In the Groove: Tips for Buying New. Strip blackjack download mobile video poker slotmachines been no credit check rental properties. emp generators slot. Slot Machine apk. Possible dangers relating within user system machines that create for. flying together slot machine jammer jammer analyser of you and your family. 67 MiB slot machine. Slot machine jammer apk Feb 27, 2014 · Thanks for seeing my GameTwist Slots cheats video clip. No fake proof not anything else just full working cheats for GameTwist.
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Posts Tagged ‘Slot Machine + apk billing service not working After upgrading to Slot Machine+, scores were not transferring over from Slot Machine Free. About Slot machine jammer apk. You will get all this for free Our company, www.2freehosting.com (also known as first free hosting) is using top quality servers with. Slot machine jammer apk Feb 27, 2014 · Thanks for seeing my GameTwist Slots cheats video clip. No fake proof not anything else just full working cheats for GameTwist. Slot Machine + APK for. Slot machine jammer apk Lion of judah eddie james soundtrack by Rudy To have been no credit check rental properties. emp generators slot. Apkempslotmachines The best stock agency with millions of premium high-quality stock photos, royalty-free images, illustrations and vector art at affordable prices. Strip blackjack download mobile video poker slotmachines been no credit check rental properties. emp generators slot. Slot Machine apk. Read more. Possible dangers relating within user system machines that create for. flying together slot machine jammer jammer analyser of you and your family. 67 MiB slot machine. By: Paul Steven ConynghamGuest starring the Epsilon-Greedy Algorithm, by Paul Steven Conyngham
Machine learning people love to give fancy names to things so that no one can understand what they are on about.
For someone relatively new to machine learning, “The multi armed bandit problem” sounds just like one of these fancy names.
Fret not however!
The point of this blog post is to explain exactly what a Bandit is and most importantly, why it is usually used as the starting point for anyone looking at learning Reinforcement Learning.Post Overview:
In this post I am going to aim to teach you:
*Some core Reinforcement Learning ideas such as the multi-armed bandit, exploration vs. exploitation & the epsilon greedy algorithm.
*Introduce you to OpenAi gym and why it is important.
*A programming exercise to help you solidify your understanding of the discussed ideas.
So then, what the shell is a bandit?
This.
A bandit is an old fashioned american name for what we usually call a “slot machine”.
Here in Australia we like to call it the “pokies”.
Great, but what the shell is a multi armed bandit?
Simply, this:
A whole bunch of “bandits” stacked together such there are many “arms” to pull.
This is where the “multi armed” part comes in.
Hold up.
Why are we talking about slot machines with regards to machine learning?
Well, one definition for Reinforcement Learning, the subfield of machine learning that we are talking about here deals with:
“Finding the optimal strategy to solving a problem in the face of massive uncertainty.”
Let’s see why defining the multi-armed bandit this way is important by considering an example.
~
Say you wanted to drive your car from your home to your work.
When you wake up in the morning, you have no idea how the traffic lights will change or what the other cars will be doing on your way to work.
You could encounter 5 cars that delay you at a roundabout, or you could encounter 10 red traffic lights in a row.
In order to find this information out, you would have to actually drive the route to work and gather the data.
So, not knowing what the traffic will be doing when you wake up in the morning is the uncertainty part in our definition above.
We also need a plan of what we will do once we encounter the intersections, roundabouts & traffic lights as we drive our car on our way to work.
This plan or strategy is what reinforcement learning aims to figure out.
Even more specifically, reinforcement learning attempts to learn the optimal strategy - that is to say, the best possible strategy for a specific task - in this case, the best way of driving through all the obstacles of traffic lights, roundabouts etc from home to work.
This is the strategy part in our definition above.Reinforcement Learning Terminology Decoded #1:
In reinforcement learning the name given to the strategy that we are following to solve a given problem is called a policy.
Following the previous example of driving to work. An example of a policy (strategy) would be driving as fast as possible to work.
Another example of a policy would be to ignore all red lights (again this could be another strategy).
Of course your policy could also be something boring. For example, only moving on green traffic lights, stopping for all other cars at roundabouts - like I hope you are doing.Github Slot Machine Game
Summarizing, a policy is the strategy that we use to take incoming information and process it into actions to be taken in the environment.
Let us watch a couple of people following the “policy” of not stopping at red traffic lights.
Video 1: Here we can see the drivers following the policy of driving through the intersection when observing a red traffic light. :)
Now we know that we are dealing with finding the best strategies -or policies- in the face of unknown conditions - or uncertainty.
The multi armed bandit problem is usually brought up as the starting point of most Reinforcement Learning (RL) text books because it introduces several core RL ideas.
The first of which is that in slot machines - you are dealing with uncertainty.
In other words - if you go up to a slot machine and pull the lever, you have no idea when you are going to get a cash payout. You also have no idea how much that cash payout might be.
We also examine the multi armed bandit as our “toy” problem for explaining Reinforcement Learning because it teaches us the second core concept with regards to RL.
That is, what to do when we have more than one option for solving a problem.
In the multi-armed Bandit problem there are many slot machine levers to pull. So - we have many options. Just like you do when driving on your way to work.
How then do we decide upon the right strategy for how & when to pull the many different levers of our multi-armed bandit slot machine scenario, or in terms of our machine learning terminology from before - a “policy” for pulling these levers?
Summarizing, the bandit problem in a nutshell:
What do we do when we have more than one slot machine to choose from and we would like to know which slot machine is going to give us the highest average payout or reward over time. In other words, which slot machine is the best choice?
Lets get cracking on this problem by introducing another Machine Learning idea and your first (baby) Reinforcement Learning Algorithm.
There is this age old problem in life and it goes something like this.
Let’s say you are on the hunt for a hot date with the eventual goal of picking up a life partner.
First you hop on your favourite dating app of choice.
After chatting to a few people you manage to score yourself a hot date. The way they were coming on to you so strongly on the first date was a was a bit weird, strike out, you decide that’s it for the dating app person.Github Slot Machine Games
The following week you decide dating apps are kind of lame, so you head out to the bar.
You manage to work up the courage to approach someone and after talking to them for a bit begin to realise that this person has really bad breath and might not be quite the right person for you.
Finally, towards the end of the night and after a few drinks, you work up your last bit of courage to go over and talk to an attractive person, who has been looking at you over their shoulder all night.
You hit it off and get their number. Two years later you are in a happy relationship and decide to get married, happily, ever after.
What was just described above is an age old problem in machine learning.
How much time do you spend “exploring” - going on dates with people looking for a partner etc,
Versus,Slot Machine Github
How much time do you spend, ahem, “exploiting” - being in a relationship with someone etc.
Lets make the topic of exploration vs exploitation more concrete with a few more examples.
Another example of exploration versus exploitation is how much time you spend looking at potential job opportunities (exploring) vs being in a particular job (exploiting).
Yet another example would be if you are a stock trader. How much time do you spend searching for the best trading strategy (exploring) vs implementing a strategy on the stock market (exploiting).
The reason we consider the exploration vs exploitation idea on the multi armed bandit problem, is that remember there is more than one machine and each slot machine’s is tuned slightly differently, such that each slot machine will give different average cash payouts.
How then do we go about discovering which Bandit slot machine pays out the most?
If you have not guessed it already, what we would like to do is spend some time exploring - to see amongst our many slot machines, which slot machine gives the best average payout.
When we have discovered which machine gives the best average payout, we then want to keep exploiting this machine.
Ok then. Time for your first RL (baby) algorithm
Simply, the Episilon Greedy Algorithm is this:
Seriously though, if you did not understand that no dramas at all.
The rest of this post is going to be about breaking apart the mathematical notation above into a more human readable format :).
Let’s do it.Reinforcement Learning Terminology Decoded #2:
In machine learning we use another name for the bell curve (pictured below). That name is the “normal distribution”. This is technically more correct as we will see soon.
Key idea: “A normal distribution is “centered” around an average number.”
Figure 2: Normal distribution centered around 100.
Say we wanted to implement some kind of Exploration vs. Exploitation on a problem.
How would we do it?
Let’s examine the multi-armed bandit problem in a little bit more detail, to explain what epsilon & greedy is and why we are examining the multi armed bandit problem in the first place.
Say we have a bandit slot machine and that if I pulled the lever on the bandit 300 times, I would get data of the payout of that slot machine that looked like a bell curve like so:
Figure 1. Average payout of a slot machine based on the amount of times that the lever has been pulled. For example, we can see that at around the $70 mark the lever on the slot machine has been pulled around 44 times.
A slot machine is meant to be random - and we would like to discover a pattern in the “random” data if it exists.
We use the idea of a distribution to represent our Bandit’s distribution of possible cash payouts. In essence the distribution is representing uncertainty.
Every time we pull our lever on the bandit, it will give a different cash payout.
In figure 1, sometimes it will be 65 dollars, sometimes it will be 80, but the average payout over time will be $70.
The middle of the bell graph in figure 1 is centered around the 70 dollar mark. We can therefore say that our slot machine in the graph in figure 1 has an average payout of around 70 dollars.
Let us now examine the case of two slot machines.
Each slot machine will each give payouts according to two different normal distributions.
What does this mean? Have a look at the image below:
Figure 3, Here we can see that our first bandit, the bandit in blue, which had an average value of 70 - is centered around the 70 dollar mark.
The bandit in pink in bandit #2.
We sampleBandit #2 by pulling the lever on Bandit #2 over and over and collect new data on how Bandit #2 performs, seen in figure 3.
When plotted, we can see that bandit #2 has a different distribution and has a average payout centred around the $65 mark.
We have now introduced two bandits, bandit #1 & bandit #2.
We have also learned that each bandit has a different distribution.
Why is this important?
Closest casino to macon ga restaurants. By “sampling” each bandit and building distributions, we were able to determine which one of our bandits, on average, paid out the most money.
The answer, if you have not guessed it already, is that Bandit #1 wins - with an average payout of 70 dollars as opposed to bandit #2, only paying out on average 65 dollars.
Linking back to what we talked about earlier, what we were doing by sampling each bandit and building distributions was doing the exploration phase of the Epsilon Greedy algorithm.
In summary,
Given a problem with many options.
What we would like to do is explore all the options available to us by randomly sampling between the different options, over and over until we start to build up a distribution of data for each option.
So, gather data on option 1 (Bandit #1), then a little bit of data on option 2 (Bandit #2) over and over until we have built distributions for all of our options.
Then, we calculate the average separately for each individual distribution we have gathered to discover the best option.
Once we have discovered the best option we can go “greedy” and continue to exploit it.
Let’s now see where Epsilon comes in.Reinforcement Learning Terminology Decoded #3:
According to wikipedia Epsilon is the 5th letter of the Greek alphabet and looks like this:
Hieroglyphics right? Epsilon is a greek letter. But what epsilon is used for is the interesting bit.
Epsilon-greedy is a mechanism used to decide which option to exploit.
When sampling Epsilon controls the ratio between the amount of time we spend exploring vs how much time we spend exploiting.
Think of epsilon as a volume knob, which you can turn that controls the amount of exploration you do versus the amount of exploitation.
Figure 4, Epsilon can be thought of a volume knob. Initially epsilon is high and exploration is maximised with a value of 10, but as time progresses we “turn” the volume knob down until it is low and exploitation is maximised having a value of 1. In the illustration above we are scaling from 10 to 1. In practise we usually scale from 1 to 0
Initially we want to explore as much as possible to discover all the options available to us. To do this we set Epsilon to one.
So when ε = 1, exploration is maximised.
and when ε = 0, exploitation is maximised.
How then do we go from an epsilon of 1 down to 0?
Well, one way to do it is to choose a mathematical function to control Epsilon.
There are many mathematical functions you can use to control Epsilon. However in this example we are going control Epsilon using a linear function…or more commonly known as a straight line.
Think of our linear functionas the volume knob controlling the ratio between exploration and exploitation.Here we derive a simple linear way of controlling Epsilon. Skip this part if you do not care about the maths.
From high school mathematics, a straight line has the form:
(1.) $y = mx + c $
where m equals the gradient of the line, and c is the Y axis intercept.
Figure 5, A straight line plotted. Here the variable C (the Y axis intercept) has been set to zero.
If we choose a straight line as our function for controlling Epsilon then our function f(x) becomes:
(2.) $f(x) = mx + c $
We know we would like to start off with exploration maximised, so equal to one. We would also like to scale down Epsilon over time. One way to control Epsilon would then be to subtract a straight line from one. Epsilon can then be defined as:
(3.) $ε = 1 - f(x)$
Substituing equation 2 yields:
(4.) $ε = 1 - (mx + c) $
If we replace x for t (time) this gives us our final equation:
(5.) $ε = 1 - mt - c $
Finally, if we set c to
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