# 1.15 Machine learning lecture 16  (Page 12/15)

So I should write down some other things first, just to ground the notations, but what I’ll do is eventually come up with an algorithm for computing V*, the optimal value function and then we’ll plug them into this and that will give us the optimal policy p*.

And so I’ll write down the algorithm in a second, but just to ground the notation, well – yeah, let’s skip that. Let’s just talk about the algorithm. So this is an algorithm called value iteration and it makes use of Bellman’s equations for the optimal policy to compute V*. So here’s the algorithm. Okay, and that’s the entirety of the algorithm and oh, you repeat the step, I guess. You repeatedly do this step.

So just to be concrete, let’s say in my MDP of 11 states, the first step is initialize V(s) equals zero, so what that means is I create an array in computer implementation, create an array of 11 elements and say set all of them to zero. Says I can initialize into anything. It doesn’t really matter.

And now what I’m going to do is I’ll take Bellman’s equations and we’ll keep on taking the right hand side of Bellman’s equations and overwriting and start copying down the left hand side. So we’ll essentially iteratively try to make Bellman’s equations hold true for the numbers V(s) that are stored along the way. So V(s) here is in the array of 11 elements and I’m going to repeatedly compute the right hand side and copy that onto V(s).

And it turns out that when you do this, this will make V(s) converge to V*(s), so it may be of no surprise because we know V* [inaudible] set inside Bellman’s equations.

Just to tell you, some of these ideas that they get more than the problem says, so I won’t prove the conversions of this algorithm. Some implementation details, it turns out there’s two ways you can do this update. One is when I say for every state s that has performed this update, one way you can do this is for every state s, you can compute the right hand side and then you can simultaneously overwrite the left hand side for every state s. And so if you do that, that’s called a sequence update. Right and sequence [inaudible], so update all the states s simultaneously.

And if you do that, it’s sometimes written as follows. If you do synchronous update, then it’s as if you have some value function, you’re at the Ith iteration or Tth iteration of the algorithm and then you’re going to compute some function of your entire value function, and then you get to set your value function to your new version, so simultaneously update all 11 values in your s space value function.

So it’s sometimes written like this. My B here is called the Bellman backup operator, so the synchronized valuation you sort of take the value function, you apply the Bellman backup operator to it and then the Bellman backup operator just means computing the right hand side of this for all the states and you’ve overwritten your entire value function.

The only way of performing these updates is asynchronous updates, which is where you update the states one at a time. So you go through the states in some fixed order, so would update V(s) for state No. 1 and then I would like to update V(s) for state No. 2, then state No. 3, and so on. And when I’m updating V(s) for state No. 5, if V(s) prime, if I end up using the values for states 1, 2, 3, and 4 on the right hand side, then I’d use my recently updated values on the right hand side. So as you update sequentially, when you’re updating in the fifth state, you’d be using values, new values, for states 1, 2, 3, and 4. And that’s called an asynchronous update.

#### Questions & Answers

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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