Simulation Study of Bandit Algorithms In this problem, we evaluate the performance of two algorithms for the multi-armed bandit problem. The general protocol for the multi-armed bandit problem with K arms and n rounds is as follows: in each round t = 1,..., n the algorithm chooses an arm At E {1,..., K} and then observes reward rt for the chosen arm. The bandit algorithm specifies how to choose the arm At based on what rewards have been observed so far. In this problem, we consider a multi-armed bandit for K = 2 arms, n = 50 rounds, and where the reward at time t is rt ~ N(At – 1,1), i.e. N(0,1) for arm 1 and N(1,1) for arm 2. (a) (4 points) Consider the multi-armed bandit where the arm At E {1, 2} is chosen accord- ing to the explore-then-commit algorithm (below) with c= 4. Let Gn = 2n=1 rt denote the total reward after n = 50 iterations. Simulate the random variable Gn a total of B = 2000 times and save the values Gb), b = 1, ..., B in a list. Report the (empirical) average pseudoregret 3 DB1 (504* – GO) (where u* is the mean of the best arm) and plot a normalized histogram of the rewards. 9 = Algorithm 1 Explore-then-Commit Algorithm input: Number of initial pulls c per arm for t= 1,...,cK : do Choose arm At = (t mod K)+1 end Let € {1,..., K} denote the arm with the highest average reward so far. for t= cK + 1, cK + 2,...,n: do | Choose arm At = end (b) (4 points) Consider the multi-armed bandit where the arm At € {1,2} is chosen accord- ing to the UCB algorithm (below) with c= 4, n = 50 rounds. Repeat the simulation in Part (a) using the UCB algorithm, again reporting the empirical) average pseudoregret and the histogram of Go for b = 1...B for B = 2000. How does the pseudoregret compare to your results from part (a)? Note: If TẠ(t) denote the number of times arm A has been chosen (before time t) and û Azt is the average reward from choosing arm A (up to time t), then use the upper con- fidence bound û A,TA(t-1) + V TA(t-1): 2 log(20) + Note also that this algorithm is slightly different than the one used in lab and lecture as we are using an initial exploration phase. = Algorithm 2 UCB Algorithm input: Number of initial pulls c per arm for t= 1, ...,cK : do | Choose arm At = (t mod K)+1 end for t = cK + 1, cK + 2...: do | Choose arm At with the highest upper confidence bound so far. end (c) (1 point) Compare the distributions of the rewards by also plotting them on the same plot and briefly justify the salient differences.

The completed table represents the values of the missing entries for the given equation y = x² - 4x + 4.

To determine the values of the missing entries and complete the table, we need to substitute the given values of x into the equation y = x² - 4x + 4 and evaluate the corresponding y-values. Let's start:

For x = 0:

y = (0)² - 4(0) + 4

y = 0 - 0 + 4

y = 4

So, the ordered pair is (0, 4).

For x = 1:

y = (1)² - 4(1) + 4

y = 1 - 4 + 4

y = 1

So, the ordered pair is (1, 1).

For x = 2:

y = (2)² - 4(2) + 4

y = 4 - 8 + 4

y = 0

So, the ordered pair is (2, 0).

For x = 3:

y = (3)² - 4(3) + 4

y = 9 - 12 + 4

y = 1

So, the ordered pair is (3, 1).

For x = 4:

y = (4)² - 4(4) + 4

y = 16 - 16 + 4

y = 4

So, the ordered pair is (4, 4).

Completing the table:

x y

0 4

1 1

2 0

3 1

4 4

Therefore, the completed table represents the values of the missing entries for the given equation y = x² - 4x + 4.

Visit here to learn more about  equation:

brainly.com/question/10413253

#SPJ11

Answer: C) $33

Step-by-step explanation:

1973 tax rate :

2% on the first $1000 income

3% on next $2000 or any part thereof ;

Brown's total income of $1800

2% of $1000

0.02 × $1000 = $20

3% of $800

0.03 × 800 = $24

Total tax = $(20 + 24) = $44

1/4 tax deduction:

(1/4) of total tax

(1/4) × $44

0.25 × $44

= $11

Total tax - tax deduction

$44 - $11 = $33

Tax amount = $33

The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

Learn more about binomial  here:

https://brainly.com/question/30339327

#SPJ11

When swerving, there are a number of factors that come into play, including traction, lean, load triangle, and being upright. Swerving in a straight line can be relatively easy, as the rider only needs to make minor adjustments to maintain balance.

When comparing swerving in a straight line to swerving in a curve, the key differences involve traction and maintaining an appropriate lean angle.
Swerving in a curve requires more traction than swerving in a straight line. Traction is essential for maintaining control of your vehicle, especially when navigating curves. As you swerve in a curve, your tires need to have a good grip on the road surface to prevent skidding or losing control.
Additionally, managing lean angles is more critical when swerving in a curve. To maintain balance and control, you must avoid leaning too much, as it can cause the vehicle to tip over or slide out. In a curve, the lean angle needs to be adjusted appropriately to match the curve's radius, while also considering your speed and road conditions.
In summary, swerving in a curve requires more traction and careful management of lean angles compared to swerving in a straight line. The load triangle and keeping the vehicle upright are important, but they are not the primary factors that make swerving in a curve more challenging than swerving in a straight line.

Visit here to learn more about Swerving:

brainly.com/question/1523159

#SPJ11

Running a 60-watt LED light bulb for 24 hours would consume 1.44 kilowatt-hours (kWh) of electricity, which, depending on the cost of electricity in your area, could range from around $0.10 to $0.30.

To calculate the cost of running a 60-watt LED light bulb for 24 hours, we need to determine the energy consumption in kilowatt-hours (kWh) and multiply it by the cost per kWh in your area.

First, convert the wattage to kilowatts by dividing it by 1000: 60 watts ÷ 1000 = 0.06 kilowatts.

Next, calculate the energy consumption by multiplying the power (0.06 kW) by the time (24 hours): 0.06 kW × 24 hours = 1.44 kWh.

The cost will vary depending on your location and the price of electricity. In the United States, the average residential electricity rate is around $0.13 per kWh. Multiplying the energy consumption (1.44 kWh) by the electricity rate ($0.13) gives us the cost: 1.44 kWh × $0.13/kWh = $0.1872.

Therefore, the cost to run a 60-watt LED light bulb for 24 hours would be around $0.10 to $0.30, depending on the specific electricity rates in your area.

Learn more about area here: https://brainly.com/question/16151549

#SPJ11

The rationing function of prices refers to ability of competitive forces of supply and demand to establish a price at which scarce goods or resources are allocated among different users or consumers.

The price serves as a mechanism,

To determine who gets access to a limited quantity of goods or resources when the demand exceeds the available supply.

When the demand for a particular good or resource is high and the supply is limited, the price tends to increase.

This increase in price acts as a signal to both consumers and producers.

On the consumer side, the higher price encourages individuals to reduce their demand or seek alternative substitutes.

As the higher price may make the good less affordable or desirable.

On the producer side, the higher price provides an incentive to produce more of the scarce good, as it becomes more profitable.

Through this interplay of supply and demand, the price helps to allocate the limited resources efficiently.

Those who value the good or resource the most and are willing to pay the higher price will be able to obtain it.

While others who are not willing or able to pay the higher price may choose to forgo the purchase.

In this way, the rationing function of prices helps to allocate resources based on individuals' willingness.

And ability to pay, ensuring that resources are distributed among those who value them the most.

Therefore, rationing function of prices refers to ability of supply and demand to establish a price at which scarce goods or resources are allocated among consumers based on their willingness and ability to pay.

Learn more about supply and demand here

brainly.com/question/27961962

#SPJ4

The rationing function of prices refers to the ability of supply and demand to establish prices which leads to an equilibrium where shortage or surplus is minimized, ensuring an efficient allocation of resources in a perfectly competitive market.

The rationing function of prices refers to the ability of the competitive forces of supply and demand to establish a price at which selling and buying occurs in a way that gross imbalance does not occur. This characteristic of a market is called allocative efficiency. In a perfectly competitive market, prices tend to be established where marginal cost crosses the demand curve. This point is sometimes regulated to ensure the firm produces the output at where marginal cost equals the price, which then benefits both consumers and the broader social interest. This situation assures consumers a higher quantity and lower price, and it results in the most efficient allocation of resources.

https://brainly.com/question/33821634

#SPJ6

The Fourier coefficient angle θ₁ of the combined trigonometric series is 2π.

To find the Fourier coefficient angle θ₁ of the combined trigonometric series for the periodic function z(t) = sin(5t) - cos(10t) - sin(20t), we need to express the function in the standard form of a Fourier series:

z(t) = Σ[Ak * cos(kωt + θk) + Bk * sin(kωt + φk)]

where Ak and Bk are the Fourier coefficients, ω is the angular frequency, and θk and φk are the phase angles.

Comparing this form to the given function z(t) = sin(5t) - cos(10t) - sin(20t), we can identify the frequencies and corresponding coefficients as follows:

For the term sin(5t):

Angular frequency ω₁ = 5

Amplitude A₁ = 1

Phase angle θ₁ = 0 (since sin(5t) does not have a phase shift term)

For the term -cos(10t):

Angular frequency ω₂ = 10

Amplitude A₂ = -1

Phase angle θ₂ = π (since cos(10t) has a phase shift of π)

For the term -sin(20t):

Angular frequency ω₃ = 20

Amplitude A₃ = -1

Phase angle θ₃ = 0 (since -sin(20t) does not have a phase shift term)

Now, to find the combined Fourier coefficient angle θ₁, we need to consider the terms that contribute to the cosine component in the series. Since sin(5t) and -sin(20t) do not have cosine components, we only need to consider the -cos(10t) term.

For the cosine term -cos(10t):

The coefficient A₂ = -1 contributes to the cosine component.

The phase angle θ₂ = π represents the phase shift.

Therefore, the combined Fourier coefficient angle θ₁ is given by:

θ₁ = θ₂ + π = π + π = 2π

Hence, the Fourier coefficient angle θ₁ of the combined trigonometric series for the periodic function z(t) = sin(5t) - cos(10t) - sin(20t) is 2π.

To learn more about coefficient here:

https://brainly.com/question/30215548

#SPJ4

Given:

Lamont has purchased 20 trading cards.

He wants to have at least 50 trading cards.

To find:

The inequality for the number of trading cards Lamont needs and solve it.

Solution:

Let x be the number of trading cards Lamont needs.

He has 20 trading cards. So,

Total cards = x + 20

It is given that, he wants to have at least 50 trading cards. It means, total card must be greater than or equal to 50.

\(x+20\geq 50\)

Subtract 20 from both sides.

\(x+20-20\geq 50-20\)

\(x\geq 30\)

Therefore, the required inequality is \(x+20\geq 50\) and solution is \(x\geq 30\).

The number of trading cards that Lamont needs will be at least 30 trading cards.

From the information given, we are informed that Lamont has purchased 20 trading cards and wants to have at least 50 trading cards.

Therefore, the number that will be needed more will be:

= 50 - 20 = 30

Therefore, he'll need at least 30 more cards.

Read related link on:

https://brainly.com/question/14058435

Given:

A figure of a circle with radius 8. The central angle of the blue sector is 60 degrees.

To find:

The area of the blue sector.

Solution:

Area of a sector is:

\(A=\pi r^2\dfrac{\theta}{360^\circ}\)

Where, r is the radius and \(\theta \) is the central angle of the sector in degrees.

Putting \(r=8, \theta=60^\circ, \pi=3.14\), we get

\(A=(3.14)\cdot (8)^2\cdot \dfrac{60^\circ}{360^\circ}\)

\(A=(3.14) \cdot (64)\cdot \dfrac{1}{6}\)

\(A=33.49333....\)

Approximate the value to the nearest tenth.

\(A\approx 33.5\)

Therefore, the area of the blue sector is about 33.5 sq. units.

Answer:

25 students didn't like any of the games

Step-by-step explanation:

20-15=5     40-10=30

20-5=25

Option (C) a sequence of statements that demonstrates the truth of an assertion is the best definition of mathematical proof.

A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.

As we know, mathematical proofs are a set of sequential statements that assist in demonstrating the truth of a proposition.

For example:

2n + 1 = 3n

If n = 1 the above expression is true.

To proof the above expression plug n = 1:

2(1) + 1 = 3(1)

2 + 1 = 3

3 = 3  (true)

Thus, option (C) a sequence of statements that demonstrates the truth of an assertion is the best definition of mathematical proof.

Learn more about the mathematical proof here:

https://brainly.com/question/15598701

#SPJ1

Answer:

Subtract everything from 180. The square boxes represent 90°.

1. 180-80-40 = 60°

2. 180-90-32 = 58°

3. 180-45-90 = 45°

4. 180-90-78 = 12°

5. 180-90-15 = 75°

6. 180-55-25 = 100°

7. 180-90-36 = 54°

8. 180-90-30 = 60°

9. 180-60-30 = 90°

Hope this helped :)

The normal model could provide a reasonable estimation again for sampling distribution of p1 and p2. D is the ideal choice. No, the normal distribution is the foundation of the 68-95-99.7 rule.

Sampling the mean distribution. The mean is the most typical kind of sample distribution. sampling the proportional distribution. The ratios in a population are the main focus of this sampling distribution. T-distribution.

When you repeat a survey or polling for all potential samples of the population, you get the probability density of a proportion. For instance, you may run your poll several times and ask 1000 cat owners which cat food they prefer.

To know more about sampling distribution visit:

https://brainly.com/question/22985950

#SPJ1

Answer:

50 degrees

Step-by-step explanation:

If angle L = 65 then the top angle for the triangle LMJ has to be 25 degrees as M is a right angle (or at least has to be for this problem to be possible)

the math to figure it out is 90+65+x=180 <-- due to triangles are 180 degrees inside which simplifies to 25 after that you just have to at 25 to itself 25+25 to get 50 which is the angle of J

Answer:

What kind of mathematics is this?

Answer:

2/13,3/13,4/13....

hope it helps

Answer:

Step-by-step explanation:

4/13=40/130

1/13=10/130

numbers between 10/130 and 40/130 are 11/130,12/130,13,130 ,...,39/130.

we can select  any three out of these.

The required value of the boat at the end of 2015 is $38,525.76.

Given that,
The value of a boat depreciates by 16% each year. at the end of 2012, the value of the boat is £65000 3 years work out the value of the boat at the end of 2015 is to be determined.

The function which is in format f(x) = aˣ , where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Let the total cost after x years be y,
According to the question,
As the price is depreciating at a rate of 16% each year the relation formed is exponential relation,
y = 65000(1 - 0.16)ˣ
Substitute x = 3 for the year 2015
y = 65000(0.86)³
y = $38,525.76

Thus, the required value of the boat at the end of 2015 is $38,525.76.

learn more about exponential function here:

brainly.com/question/15352175

#SPJ2

Answer:Ten dollars per hour

Step-by-step explanation:

50 hour =500 dollars

1 hour = ?

Using the criss cross method we multiply one hour by five hundred dollars and divide by fifty dollars.

?=(1 hour×500 dollars)/50 hour

?= 500 dollars/50

?=10 dollars per hour

Answer:

$10

Step-by-step explanation:

$500/50= 10

He needs to earn $10 an hour x the 50 hours = $500

Answer:

I believe its -36

Step-by-step explanation:

-36+10=-26

-26/2= -13

Answer:

-36

Step-by-step explanation:

(x+10)/2 = -13

-13 times 2= -26

-26-10= -36

check

-36+10= -26

-26/2= -13

Reference angle is defined as the smallest positive angle that can be made with the x-axis. In order to find the reference angle for a given angle, we follow these steps.

If the given angle is positive and greater than or equal to 360°, subtract 360° from the given angle until it becomes less than 360°.2. If the given angle is negative, add 360° to the given angle until it becomes positive. Since the given angle is negative, we need to add 360° to it until it becomes positive.

-75° + 360°

= 285

285° is greater than 180°, so we subtract it from 360° to get the reference angle.

Reference angle = 360° - 285°

= 75°

Thus, the reference angles for the given angles are:

(c) 75°.

To know more about equal visit:

https://brainly.com/question/33293967

3SPJ11

Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

Answer:

30.00

Step-by-step explanation:

Step-by-step explanation:

m < CAD = 180 - ( 40 + 57 ) = 83

When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.

Learn more about correlation here

https://brainly.com/question/4219149

#SPJ4

Answer:

Step-by-step explanation:

Use the "point-slope" formula for the equation of a straight line,

y - k = m(x - h)

Here the slope, m, is 3 and the line passes through (h, k):  (-4, -7), so the proper equation in this case is

y - (-7) = 3(x + 4), or:

y + 7 = 3(x + 4).

If you wish you may rewrite this equation in slope-intercept form, as follows:

y = 3x - 7 + 12, or y = 3x + 5

Answer:

sum of 22nd = 1,428.05

sum of 23 to 40 is 932.53

Step-by-step explanation:

A(n)=20(1.1)^n-1

20 is the first term or a1

1.1 is the common ratio or r

A(22) = 20(1.1)^22-1

22nd term = 20(1.1)^21

22nd term = 148.00

sum of geometric sequence

formula

Sn = a1(1-r^n)/1-r

Sn = sum

a1 = first term

n = number of term

r = constant ratio

sum of 22nd = 1,428.05.

23 to 40 is 17 terms

Sequence: 23, 25.3, 27.83, 30.613, 33.6743, 37.04173, 40.745903 ...

The 17th term: 105.684378686

Sum of the first 17 terms: 932.528165548

socratic

miniwebtoolcomgeometricsequencecalculator

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

Antonio is working with a new geometric series generated by the equation that is

\(A_{n}=20(1.1)^n-1.\)

His sister challenged him to find the sum of the first 22 terms will be given as

\(Sn = \dfrac{a(r^n - 1) }{ (r - 1)}\)

We have

a = 20

r = 1.1

n = 22

Then

\(\rm S_n = \dfrac{20(1.1^{22} - 1) }{ (1.1 - 1)}\\\\\\S_n = \dfrac{20(8.14 - 1) }{ 0.1}\\\\\\S_n = \dfrac{20*7.14 }{0.1}\\\\\\S_n = 1428.05\)

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

More about the series link is given below.

https://brainly.com/question/10813422

The 12.04m is far from the base to wall.

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the number system whose digits are used to represent numbers and the number system in which logarithms are defined.

Let the base of the 17ft long ladder be placed x ft away from the wall so that it exactly reaches the top of a 12- foot tall wall.

By Pythagorean theorem

12²+X²=17²

x²=17²-12²=145

x=√145=12.04

To learn more about   base of the wall refer to:

https://brainly.com/question/18206420

#SPJ1

Answer:

C) 1 ¼

Step-by-step explanation:

.25 = ⁴/⁴ ÷ .25 = ¼

ñññññ

Answer:

The choice C)

\(1 \frac{1}{4} \)

Step-by-step explanation:

\(1.25 = \frac{5}{4} = 1 \frac{1}{4} \)

I hope I helped you^_^