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ASSIGNMENT

机器学习理论代写 CHAPTER 4 Note that you should not be using aids such as mathexchange to solve these problems. Better to work on them alone, get stuck,

CHAPTER 4

Note that you should not be using aids such as mathexchange to solve these problems. Better to work on them alone, get stuck, and then get help from other students who can provide helpful hints that still allow you to have that “ah ha!” moment, which expands your brain. Start early.

Exercise 4.1.

Prove that OSD in Example 4.11 (lecture notes) with x₁ = 0 is exactly the Follow the-Leader strategy for that particular problem. (Same as Exercise 4.1 in lecture notes.)

CHAPTER 5 机器学习理论代写

Exercise 5.2.

From course notes:. Extend the proof of Theorem 5.1 to an arbitrary norm | |·| | to measure the diameter of V and with | |g_t| |_∗ ≤ L.

Exercise 5.3.

From course notes:. Assume f and g are proper, convex, and closed and satisfy f(x) ≤ g(x) for all x. Prove that f^∗(θ) ≥ g^∗(θ) for all θ.

Exercise 5.4.

From course notes:. Assume f is even, i.e., f(x) = f(−x). Prove that f^∗ is even.

CHAPTER 6 机器学习理论代写

Exercise 6.1.

Problem 6.9 in course notes: Derive the EG update rule and regret bound in the case that the algorithm starts from an arbitrary vector x₁ in the probability simplex.

Exercise 6.3.

Implement Exponentiated Gradient (EG) and evaluate its regret in two different cases for k=2 experts. Case 1: Feed it data from two experts whose losses are equal in distribution. Case 2: Feed it data from two experts where the loss of the first expert is less on average than the loss for the second expert. Have losses bounded in [0,1] in both cases. Plot regret as a function of the number of rounds T.

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