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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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