Help solving equation

[JohnnyCowboy1098]

I have an equation here that describes how to choose a move during a training game of tic-tac-toe for an AI. Here it is. τ is a temperature value. I wasn't really sure where else to post this.

 

π(500)=Pr(500) = e^500/τ

                           --------

                            n_s

                           ∑e^500_i /τ

                           i=1

[tarfeef101]

5 minutes ago, JohnnyCowboy1098 said:

I have an equation here that describes how to choose a move during a training game of tic-tac-toe for an AI. Here it is. τ is a temperature value. I wasn't really sure where else to post this.

 

π(500)=Pr(500) = e^500/τ

                           --------

                            n_s

                           ∑e^500_i /τ

                           i=1

That should just be the sum from i=2 to n sub s, since 500i/T is just the numerator at i=1.

 

unless of course that dotted line isn't division

[JohnnyCowboy1098]

2 minutes ago, tarfeef101 said:

That should just be the sum from i=2 to n sub s, since 500i/T is just the numerator at i=1.

 

unless of course that dotted line isn't division

any chance you could explain that in terms to someone who knows who summation works but the extent of their mathematical knowledge is pre algebra?

[tarfeef101]

1 minute ago, JohnnyCowboy1098 said:

any chance you could explain that in terms to someone who knows who summation works but the extent of their mathematical knowledge is pre algebra?

So, you know the first term of the sum is for i=1. So, subbing that in, we get the term (e^(500/t) / e^((500*1)/t)), which is just (e^(500/t)) divided by itself. which is 1. so, I guess it is actually 1 plus the sum from 2 to n_s

[tarfeef101]

Oh hold on, that sum isn't for the whole thing is it... 

 

Stupid mobile version formatting was all weird. Just got on my desktop.

 

okay, so you want the value of the denominator, which is itself a sum. I can't help without knowing the values on n_s and T, or at least what they approach (is n or t always really big or really tiny)

[JohnnyCowboy1098]

4 minutes ago, tarfeef101 said:

Oh hold on, that sum isn't for the whole thing is it... 

 

Stupid mobile version formatting was all weird. Just got on my desktop.

 

okay, so you want the value of the denominator, which is itself a sum. I can't help without knowing the values on n_s and T, or at least what they approach (is n always really big or really tiny)

My guess is that the temperature is 1/2, but it could be 1 as well, and I think n is supposed to be endless, or approaching infinity?

[tarfeef101]

1 minute ago, JohnnyCowboy1098 said:

My guess is that it is 1/2, but it could be 1 as well, and I think n is supposed to be endless, or approaching infinity?

okay, if that is the case (n approachin infinity), then the sum diverges, and this is turning into MATH 138 all over again...

 

also what is .5 or 1?

[JohnnyCowboy1098]

1 minute ago, tarfeef101 said:

okay, if that is the case (n approachin infinity), then the sum diverges, and this is turning into MATH 138 all over again...

 

also what is .5 or 1?

the temperature value or τ

[tarfeef101]

So, basically that sum cannot be finitely expressed, because it is infinitely large (pls mathies don't hate on that, no need to explain calculus to this man).

 

So, if you have a finite number divided by something infinitely huge, that'll be essentially zero. 

[JohnnyCowboy1098]

2 minutes ago, tarfeef101 said:

So, basically that sum cannot be finitely expressed, because it is infinitely large (pls mathies don't hate on that, no need to explain calculus to this man).

 

So, if you have a finite number divided by something infinitely huge, that'll be essentially zero. 

I'm gonna give you a link so you can have a look at the paper i got this from

 

http://www.cs.dartmouth.edu/~lorenzo/teaching/cs134/Archive/Spring2009/final/PengTao/final_report.pdf

[tarfeef101]

9 minutes ago, JohnnyCowboy1098 said:

I'm gonna give you a link so you can have a look at the paper i got this from

 

http://www.cs.dartmouth.edu/~lorenzo/teaching/cs134/Archive/Spring2009/final/PengTao/final_report.pdf

is this what you're trying to understand (sorry for the delay, responded in the wrong post)

[JohnnyCowboy1098]

1 minute ago, tarfeef101 said:

is this what you're trying to understand (sorry for the delay, responded in the wrong post)

yes

[JohnnyCowboy1098]

i just had a value i wanted to sub in for the s values

[tarfeef101]

1 minute ago, JohnnyCowboy1098 said:

i just had a value i wanted to sub in for the s values

okay, you did not interpret this algorithm properly (sorry).

 

I suggest you gain some experience with both calculus, and simpler AI methods like the minimax discussed in the intro of that paper.

 

What I will tell you about what you did wrong was a) n does not approach infinity. From what I see, this is a 1-move depth algorithm, meaning the value of a given move is determined by the "probability of winning" or s-value of the afterstates immediately after executing a move. This will make the sum finite, and btw that sum is between the numerator and infinity (there is a mathematical explanation, but you really should learn about sums more first).

 

Then there is more (but simpler) logic dictating what move to actually do, as what I described above is all "theoretical", the computer essentially simulates games until it decides what is best, then actually makes a move.

 

main point is I'm very glad you're interested in this stuff, but you have some more material to cover before tackling something like this.

[JohnnyCowboy1098]

5 minutes ago, tarfeef101 said:

okay, you did not interpret this algorithm properly (sorry).

 

I suggest you gain some experience with both calculus, and simpler AI methods like the minimax discussed in the intro of that paper.

 

What I will tell you about what you did wrong was a) n does not approach infinity. From what I see, this is a 1-move depth algorithm, meaning the value of a given move is determined by the "probability of winning" or s-value of the afterstates immediately after executing a move. This will make the sum finite, and btw that sum is between the numerator and infinity (there is a mathematical explanation, but you really should learn about sums more first).

 

Then there is more (but simpler) logic dictating what move to actually do, as what I described above is all "theoretical", the computer essentially simulates games until it decides what is best, then actually makes a move.

 

main point is I'm very glad you're interested in this stuff, but you have some more material to cover before tackling something like this.

Thank you so much, I have a guy i'm communicating with at a university, and he might not understand I have such a limited knowledge, but here's my paper I have written on the subject, could you take a look? https://docs.google.com/document/d/12sUhoMk31_Wsry56JyHu8FfEoYIfEN-IQF35K_xK-ig/edit

[tarfeef101]

5 minutes ago, JohnnyCowboy1098 said:

Thank you so much, I have a guy i'm communicating with at a university, and he might not understand I have such a limited knowledge, but here's my paper I have written on the subject, could you take a look? https://docs.google.com/document/d/12sUhoMk31_Wsry56JyHu8FfEoYIfEN-IQF35K_xK-ig/edit

Well I can say that setup looks to be very similar to theirs... Best to reword it in the way you actually think about the problem (that language and notation is not what I expect most people to think like).

 

As for the content, I am currently procrastinating for 2 exams right now, so probably not going to take an in depth look unless you want some help after wednesday.

 

What I can say is I don't advise trying to replicate or modify their algorithm. For me, the best way to start an AI project is to think: what would I do? Then ask: why?

 

From there, you need to figure out what factors led to you making your decision, and figure out how to quantify them.

 

Here is the site for my school's CS department, and a link to their first year CS course: https://www.student.cs.uwaterloo.ca/~cs135/

 

I advise reading through the slides, and if you want to keep learning, look at CS 136, then 246 if you blaze through it (just change the number in the URL). These don't teach you AI, but rather give you the tools to figure it out by yourself (which I had fun with for that CS 246 project, let me tell you). Googling various design methods for AI, or possibly asking for some guidance from your other university contact may prove beneficial to you.

 

[JohnnyCowboy1098]

2 minutes ago, tarfeef101 said:

Well I can say that setup looks to be very similar to theirs... Best to reword it in the way you actually think about the problem (that language and notation is not what I expect most people to think like).

 

As for the content, I am currently procrastinating for 2 exams right now, so probably not going to take an in depth look unless you want some help after wednesday.

 

What I can say is I don't advise trying to replicate or modify their algorithm. For me, the best way to start an AI project is to think: what would I do? Then ask: why?

 

From there, you need to figure out what factors led to you making your decision, and figure out how to quantify them.

 

Here is the site for my school's CS department, and a link to their first year CS course: https://www.student.cs.uwaterloo.ca/~cs135/

 

I advise reading through the slides, and if you want to keep learning, look at CS 136, then 246 if you blaze through it (just change the number in the URL). These don't teach you AI, but rather give you the tools to figure it out by yourself (which I had fun with for that CS 246 project, let me tell you). Googling various design methods for AI, or possibly asking for some guidance from your other university contact may prove beneficial to you.

 

OK, sorry to take up your time, good luck on your exams:) I am just trying to get this paper done also, as it is due two days from now, but I would love to talk again after Wednesday. I will definitely look into that link.

[tarfeef101]

Just now, JohnnyCowboy1098 said:

OK, sorry to take up your time, good luck on your exams:) I am just trying to get this paper done also, as it is due two days from now, but I would love to talk again after Wednesday. I will definitely look into that link.

my pleasure. I'm sure you'll do well. Looks to me like this is for High School, and most don't even get into CS, let alone machine learning.