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Both value iteration and policy iteration are standard algorithms for solving MDPs, and there isn't currently universal agreement over which algorithm is better.For small MDPs, policy iteration is often very fast and converges with very few iterations. However, for MDPs with largestate spaces, solving for V π explicitly would involve solving a large system of linear equations, and could be difficult. In these problems,value iteration may be preferred. For this reason, in practice value iteration seems to be used more often than policy iteration.

Learning a model for an mdp

So far, we have discussed MDPs and algorithms for MDPs assuming that the state transition probabilities and rewards are known. In many realistic problems,we are not given state transition probabilities and rewards explicitly, but must instead estimate them from data. (Usually, S , A and γ are known.)

For example, suppose that, for the inverted pendulum problem (see problem set 4), we had a number of trials in the MDP, that proceeded as follows:

s 0 ( 1 ) a 0 ( 1 ) s 1 ( 1 ) a 1 ( 1 ) s 2 ( 1 ) a 2 ( 1 ) s 3 ( 1 ) a 3 ( 1 ) ... s 0 ( 2 ) a 0 ( 2 ) s 1 ( 2 ) a 1 ( 2 ) s 2 ( 2 ) a 2 ( 2 ) s 3 ( 2 ) a 3 ( 2 ) ... ...

Here, s i ( j ) is the state we were at time i of trial j , and a i ( j ) is the corresponding action that was taken from that state. In practice, each of the trials above might be run until the MDP terminates(such as if the pole falls over in the inverted pendulum problem), or it might be run for some large but finite number of timesteps.

Given this “experience” in the MDP consisting of a number of trials, we can then easily derive the maximum likelihood estimates for the statetransition probabilities:

P s a ( s ) #times took we action a in state s and got to s #times we took action a in state s

Or, if the ratio above is “0/0”—corresponding to the case of never having taken action a in state s before—the we might simply estimate P s a ( s ' ) to be 1 / | S | . (I.e., estimate P s a to be the uniform distribution over all states.)

Note that, if we gain more experience (observe more trials) in the MDP, there is an efficient way to update our estimated state transition probabilities usingthe new experience. Specifically, if we keep around the counts for both the numerator anddenominator terms of  [link] , then as we observe more trials, we can simply keep accumulating those counts. Computing the ratio of these countsthen given our estimate of P s a .

Using a similar procedure, if R is unknown, we can also pick our estimate of the expected immediate reward R ( s ) in state s to be the average reward observed in state s .

Having learned a model for the MDP, we can then use either value iteration or policy iteration to solve the MDP using the estimated transition probabilitiesand rewards. For example, putting together model learning and value iteration, here is one possible algorithm for learning in an MDP with unknown state transitionprobabilities:

  1. Initialize π randomly.
  2. Repeat {
    1. Execute π in the MDP for some number of trials.
    2. Using the accumulated experience in the MDP, update our estimates for P s a (and R , if applicable).
    3. Apply value iteration with the estimated state transition probabilities and rewards to get a new estimated value function V .
    4. Update π to be the greedy policy with respect to V .
  3. }

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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
How can I make nanorobot?
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
how can I make nanorobot?
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.
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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