THE KNOWLEDGE GRADIENT IN DYNAMIC PROGRAMMING
where
0XG'n(Sn,x) = C ( 5 n , x ) | 7 E ^ n + 1 ( ? ' n ) .
359
(17.16)
n
To understand this, it is useful to talk through the steps. If we are in state S and choose
action x, we would then observe a random qu

BAYESIAN MODELING FOR DYNAMIC PRICING
239
is, there is a price p for which / i (p) = $2 (p) = / Substituting this price into (11.7)
gives us
q^
1
=
Qnfxn+\l-f)
qnfXn+1(l
i-x71
~ / ) 1 _ X " + 1 + (1 - qn) F " + 1 ( l - / ) 1 _ J f n + 1
qnfXn+\l-!)l-Xn+1

AREAS OF APPLICATION
9
Who are the best hitters that you should choose for your baseball team? It is
necessary to see how a player hits in game situations, and of course these are
very noisy observations.
What plays work the best for your football team?

ORIE 3800: Information Systems and Analysis
ORIE 3800
Aug 22, 2012
Product Pricing
We would like to price airline tickets so as
to maximize revenue.
We learn about demand for a ight as we
sell tickets.
The information collected depends on how
we price eac

ORIE 3800: Information Systems and Analysis
This course will show you how to make decisions about information, and how decisions about
information affect the world at large. We will consider questions such as:
How much time should a venture capitalist sp

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation 3
September 17, 2012
Question 1:
Normal distribution with unknown mean: a random sample of n students is drawn from a large
population, and their weights are measured. The average weight of th

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation Solution
November 12, 2012
Question 1 Multi-armed Bandit Problem in nite number of steps
A computer receives a string of documents, where documents are coming from some distribution. Every tim

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation
November 26, 2012
Question 1
Two restaurants (A and B) have the same prior probability of being the better place. Individuals
receive a private signal with precision q = 3/4. The rst two indiv

THE BAYESIAN VIEW
39
is better than another lineup that includes three from the same group with two
different people. If the scoring of these five people is higher than we had
expected, we would probably raise our belief about the other group, since there

UPDATING FOR NON-GAUSSIAN PRIORS
49
observation n + 1 belongs to category k, we increment oQ by 1 and leave the other
components of an unchanged.
2.3.5 Learning an Unknown Variance*
Our last learning model takes us back to the basic setting of one-dimensi

A BRIEF REVIEW OF LINEAR REGRESSION
189
Just as [i is a random variable (our truth), so is #, which is the truth about the effect
of each feature. We learned that we get tremendous benefits from exploiting the
covariance between two alternatives. The cova

LARGER SETS
209
drugs in the same class will be correlated. If a patient reacts adversely to sensitizers,
all drugs of this type will tend to perform poorly. In any case, however, our prior is not
able to capture all the nuances of the problem. Instead, t

OBJECTIVE FUNCTIONS
169
7.5.1 Designing Versus Controlling
We have already compared two broad settings in which optimal learning arises: offline
learning, where we conduct a series of measurements to design a process or system
under some sort of measureme

UPPER CONFIDENCE BOUNDING
149
vides tight minimax bounds on the regret for problems with continuous arms,
but these are exponential in the number of dimensions.
Response-surface bandits - There are many applications where our beliefs about the
value of di

THE KNOWLEDGE GRADIENT FOR SOME NON-GAUSSIAN DISTRIBUTIONS
109
where N+1 is the number of units of product x ordered on the next day. We assume
that iV+1 ~ Poisson (Xx). If we are looking for the largest rate, the definition of
the KG factor is once again

THE PROBLEM OF PRIORS
119
Figure 5.8 The effect of the prior on the search process: (a) Unbiased prior, (b) Resulting
measurements, (c) Prior that is biased low. (d) A low prior produces measurements focused
around whatever point is chosen first, (e) Prio

PROBLEMS
129
mean 0.267 and standard deviation of 0.10. Finally assume that we are going to
approximate the observed batting average from at least*! 0 at-bats as normally
distributed with mean:
H
Wrr
where H is the number of hits and m is the number of at

KNOWLEDGE GRADIENT FOR CORRELATED BELIEFS
99
Now we are trying to find the best price for our laptop. We start with an initial
guess of the sales volume we will for prices in $100 increments from 700 to
1200. We start at $1100, and sales are much lower t

MEASUREMENT POLICIES
79
for 0 < c < 1. If we explore, we would choose measurement x with probability
1/|#|. This means that in the limit, the number of times we will measure x is given
by
oo
'
n=l
'
This assures us that we will estimate each measurement x

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation
November 05, 2012
Create graphs for the Sequential Comparison with a Standard problem
Problem setting recall: We consider the problem of comparison with a standard, but now in a
sequential set

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation
November 05, 2012
Create graphs for the Sequential Comparison with a Standard problem
Problem setting recall: We consider the problem of comparison with a standard, but now in a
sequential set

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation
November 12, 2012
Question 1 Multi-armed Bandit Problem in nite number of steps
A computer receives a string of documents, where documents are coming from some distribution. Every time when a