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In policy iteration, we initialize the policy p randomly, so it doesn’t matter. It can be the policy that always goes north or the policy that takes actions random or whatever. And then we’ll repeatedly do the following. Okay, so that’s the algorithm.

So the algorithm has two steps. In the first step, we solve. We take the current policy p and we solve Bellman’s equations to obtain Vp. So remember, earlier I said if you have a fixed policy p, then yeah, Bellman’s equation defines this system of linear equations with 11 unknowns and 11 linear constraints. And so you solve that linear system equation so you get the value function for your current policy p, and by this notation, I mean just let V be the value function for policy p.

Then the second step is you update the policy. In other words, you pretend that your current guess V from the value function is indeed the optimal value function and you let p(s) be equal to that out max formula, so as to update your policy p.

And so it turns out that if you do this, then V will converge to V* and p will converge to p*, and so this is another way to find the optimal policy for MDP.

In terms of tradeoffs, it turns out that – let’s see – in policy iteration, the computationally expensive step is this one. You need to solve this linear system of equations. You have n equations and n unknowns, if you have n states. And so if you have a problem with a reasonably few number of states, if you have a problem with like 11 states, you can solve the linear system equations fairly efficiently, and so policy iteration tends to work extremely well for problems with smallish numbers of states where you can actually solve those linear systems of equations efficiently.

So if you have a thousand states, anything less than that, you can solve a system of a thousand equations very efficiently, so policy iteration will often work fine. If you have an MDP with an enormous number of states, so we’ll actually often see MDPs with tens of thousands or hundreds of thousands or millions or tens of millions of states. If you have a problem with 10 million states and you try to apply policy iteration, then this step requires solving the linear system of 10 million equations and this would be computationally expensive. And so for these really, really large MDPs, I tend to use value iteration.

Let’s see. Any questions about this?

Student: So this is a convex function where – that it could be good in local optimization scheme.

Instructor (Andrew Ng) :Ah, yes, you’re right. That’s a good question: Is this a convex function? It actually turns out that there is a way to pose a problem of solving for V* as a convex optimization problem, as a linear program. For instance, I can break down the solution – you write down V* as a solution, so linear would be the only problem you can solve. Policy iteration converges as gamma T conversion. We’re not just stuck with local optimal, but the proof of the conversions of policy iteration sort of uses somewhat different principles in convex optimization. At least the versions as far as I can see, yeah. You could probably relate this back to convex optimization, but not understand the principle of why this often converges.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket 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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