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So it turns out that there’s a version of Bellman’s equations for V* as well and so this is also called Bellman’s equations for V* rather than for Vp and I’ll just write that down. So this says that the optimal payoff you can get from the state s is equal to – so our [inaudible] are multi here, so let’s see. Just for starting off in the state s, you’re going to get your immediate R(s) and then depending on what action a you take your expected total payoff will be given by this. So if I take an action a in some state s, then with probability given by P subscript (s; a) of s prime, by this probability our transition of state s prime, and when we get to the state s prime, I’ll expect my total payoff from there to be given by V*(s) prime because I’m now starting to use the s prime.

So the only thing in this equation I need to fill in is where is the action a, so in order to actually obtain the optimal expected payoff, and to actually obtain the maximum or the optimal expected total payoff, what you should choose here is the max over our actions a, choose your action a that maximizes the expected value of your total payoffs as well.

So it just makes sense. There’s a version of Bellman’s equations for V* rather than Vp and I’ll just say it again. It says that my optimal expected total payoff is my immediate reward plus, and then the best action it can choose, the max over all actions a of my expected future payoff.

And these also lead to my definition of p*, which is let’s say I’m in some state s and I want to know what action to choose. Well, if I’m in some state s, I’m gonna get here an immediate R(s) anyway, so what’s the best action for me to choose is whatever action will enable me to maximize the second term, as well as if my robot is in some state s and it wants to know what action to choose, I want to choose the action that will maximize my expected total payoff and so p*(s) is going to define as R(max) over actions a of this same thing.

I could also put the gamma there, but gamma is just a positive. Gamma is almost always positive, so I just drop that because it’s just a constant scale you go through and doesn’t affect the R(max).

And so, the consequence of this definition is that p* is actually the optimal policy because p* will maximize my expected total payoffs.

Cool. Any questions at this point? Cool. So what I’d like to do now is talk about how algorithms actually compute high start, compute the optimal policy. I should write down a little bit more before I do that, but notice that if I can compute V*, if I can compute the optimal value function, then I can plug it into this equation and then I’ll be done. So if I can compute V*, then you are using this definition for p* and can compute the optimal policy.

So my strategy for computing the optimal policy will be to compute V* and then plug it into this equation and that will give me the optimal policy p*. So my goal, my next goal, will really be to compute V*.

But the definition of V* here doesn’t lead to a nice algorithm for computing it because let’s see – so I know how to compute Vp for any given policy p by solving that linear system equation, but there’s an exponentially large number of policies, so you get 11 states and four actions and what the number of policies is froze to the par of 11. This is of a huge space of possible policies and so I can’t actually exhaust the union of all policies and then take a max on [inaudible].

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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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