ORIE 3800 Homework 3: Solutions
Jiayang Gao
Due Feb.27, 2015
1. Solution.
Lets first calculate the posterior given signal s = s. By Bayes Theorem, the posterior
is given by
P (
= 1|
s = s) =
f (
s =
ORIE 3800: Assignment 1
Instructor: Krishnamurthy Iyer
February 5, 2016
Due on: February 12, 2016, 12pm
Please submit your homework in the dropbox in Rhodes 2nd floor lobby.
1. Suppose you have a fair
ORIE 3800: Assignment 3 Solutions
Instructor: Krishnamurthy Iyer
Spring 2016
1. Throughout, let H be the event that the outcome of the gamble is heads, and T be the
event that the outcome is tails. We
ORIE 3800 Homework 3
Due Thursday September 20, 2012
[Posted September 16]
Please put your nished homework in the dropbox by Thursday at noon. Refer to the syllabus for the
policy on late homeworks.
1
ORIE 3800: Homework 2
Out: February 3
Instructor: Matthias Poloczek
Due: February 10
For this homework assignment pair submissions are allowed. Please add your name(s) and netid(s) and
submit your hom
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
ORIE 3800: Assignment 3
Instructor: Krishnamurthy Iyer
February 26, 2016
Due on: Friday, March 4, 12pm
Please submit your homework in the dropbox in Rhodes 2nd floor lobby.
1. Continuing on the theme
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
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
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, a
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
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 p
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
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 observat
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 proba
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
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 ma
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 larg
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
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
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
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
'
T
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
abl
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
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
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 document