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And so once you’ve found V*, we can use this equation to find the optimal policy ?* and the last piece of this algorithm was Bellman’s equations where we know that V*, the optimal sum of discounted rewards you can get for State S, is equal to the immediate reward you get just for starting off in that state +G(for the max over all the actions you could take)(your future sum of discounted rewards)(your future payoff starting from the State S(p) which is where you might transition to after 1(s). And so this gave us a value iteration algorithm, which was essentially V.I.

I’m abbreviating value iteration as V.I., so in the value iteration algorithm, in V.I., you just take Bellman’s equations and you repeatedly do this. So initialize some guess of the value functions. Initialize a zero as the sum rounding guess and then repeatedly perform this update for all states, and I said last time that if you do this repeatedly, then V(s) will converge to the optimal value function, V*(s) and then having found V*(s), you can compute the optimal policy ?*.

Just one final thing I want to recap was the policy iteration algorithm in which we repeat the following two steps. So let’s see, given a random initial policy, we’ll solve for Vp. We’ll solve for the value function for that specific policy. So this means for every state, compute the expected sum of discounted rewards for if you execute the policy ? from that state, and then the other step of policy iteration is having found the value function for your policy, you then update the policy pretending that you’ve already found the optimal value function, V*, and then you repeatedly perform these two steps where you solve for the value function for your current policy and then pretend that that’s actually the optimal value function and solve for the policy given the value function, and you repeatedly update the value function or update the policy using that value function. And last time I said that this will also cause the estimated value function V to converge to V* and this will cause p to converge to ?*, the optimal policy.

So those are based on our last lecture [inaudible] MDPs and introduced a lot of new notation symbols and just summarize all that again. What I’m about to do now, what I’m about to do for the rest of today’s lecture is actually build on these two algorithms so I guess if you have any questions about this piece, ask now since I’ve got to go on please. Yeah.

Student: [Inaudible] how those two algorithms are very different?

Instructor (Andrew Ng) :I see, right, so yeah, do you see that they’re different? Okay, how it’s different. Let’s see. So well here’s one difference. I didn’t say this ‘cause no longer use it today. So value iteration and policy iteration are different algorithms. In policy iteration in this step, you’re given a fixed policy, and you’re going to solve for the value function for that policy and so you’re given some fixed policy ?, meaning some function mapping from the state’s actions. So give you some policy and whatever. That’s just some policy; it’s not a great policy. And in that step that I circled, we have to find the ? of S which means that for every state you need to compute your expected sum of discounted rewards or if you execute this specific policy and starting off the MDP in that state S.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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
I'm not sure why it wrote it the other way
I got X =-6
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
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Machine learning. OpenStax CNX. Oct 14, 2013 Download for free at http://cnx.org/content/col11500/1.4
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