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University of California, Berkeley *
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Course
C102
Subject
Computer Science
Date
Apr 29, 2024
Type
Pages
11
Uploaded by GeneralProtonBeaver21 on coursehero.com
4/27/24, 7:24 PM
View Submission | Gradescope
https://www.gradescope.com/courses/711377/assignments/4324125/submissions/244847232
1/11
Q1
1 Point
Calculate the Hoeffding bound for a variable which is the sample mean of 10 random variables which are each bounded between 3 and 8. In other words, compute a bound for the following probability where is the expected value of .
Z
P
(
Z
−
μ
≥
t
)
μ
Z
10
10
E
[
X
]
i
25
2
1
t
>=0
min
e
10
t
E
[
e
]
t
(
Z
−
μ
)
exp
−
(
5
4
t
2
)
4/27/24, 7:24 PM
View Submission | Gradescope
https://www.gradescope.com/courses/711377/assignments/4324125/submissions/244847232
2/11
Q2 Bandits
2 Points
Let be the set of arms in the setting of the bandits problem. For each arm , let the random variable be the random reward received for pulling arm at time and let be the expected reward from pulling arm . Finally, let the random variable be the arm pulled at time (so is the reward received at time ).
All expectations (e.g., , ) are taken over the randomness in the payouts as well as the arm pulled at each timestep.
Q2.1 Regret
1 Point
Select all of the definitions which are true.
A
a
∈
A
X
i
a
a
i
μ
=
a
E[
X
]
i
a
a
A
i
i
X
i
A
i
i
E[
X
]
i
a
E[
X
]
i
A
i
X
i
a
A
i
The regret is .
R
(
t
)
X
−
X
i
=1
∑
t
(
a
∈
A
max
i
a
i
A
i
)
The regret is .
R
(
t
)
μ
−
X
i
=1
∑
t
(
a
∈
A
max
a
i
A
i
)
The regret is .
R
(
t
)
X
− E[
X
]
i
=1
∑
t
(
a
∈
A
max
i
a
i
A
i
)
The regret is .
R
(
t
)
μ
− E[
X
]
i
=1
∑
t
(
a
∈
A
max
a
i
A
i
)
The regret is R
(
t
)
t
μ
−
a
∈
A
max
a
X
i
=1
∑
t
i
A
i
The regret is R
(
t
)
t
μ
−
a
∈
A
max
a
E[
X
]
i
=1
∑
t
i
A
i
4/27/24, 7:24 PM
View Submission | Gradescope
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3/11
Q2.2 Expected Regret and Pseudo-Regret
1 Point
Select all of the definitions which are true.
4/27/24, 7:24 PM
View Submission | Gradescope
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4/11
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p(1, 2) = 0.1
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Email WeBWork TA
p(1,3)= 0.05
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