Questions

25S-STATS-102B-LEC-3 S25 Midterm Exam- Requires Respondus LockDown Browser

Multiple choice

Continuing from the question above, one may introduce a step length parameter, 𝛼 , into the formula as follows: 𝑊 𝑘 = 𝑊 𝑘 − 1 + 𝛼 𝑑 𝑘 − 1 Please select all the correct answers below.

Options

A.It is necessary to normalize the direction vector d when introducing the length parameter.

B.We may set 𝛼 = 1 / 𝑘 at the _k-th iteration, which shortens the step length as the process progresses. Fortunately, this approach will still reach the optimum in practice, as long as the iterations continue.

C.Adding a length parameter may result in more iterations to reach an optimum.

D.When applying the diminishing step-size rule, the total distance traveled by the algorithm tends to infinity, provided the process continues indefinitely.

E.The length parameter should be a value between 0 and 1.

F.The length parameter can be any positive value.

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Step-by-Step Analysis

On this question, we’re evaluating statements about introducing a step length parameter α into the iterative update W_k = W_{k-1} + α d_{k-1}. Option 1: It is necessary to normalize the direction vector d when introducing the length parameter. - This claim is not generally true. The step length α already controls how far you move along direction d; you can leave d unnormalized and choose α accordingly, or you can normalize d and keep α as a separate scale. Normalization of d is not a strict necessity for introducing α, though in practice some algorithms choose to work with unit direction for stability. What matters most is the product α d, not whether d itself is normalized. Option 2: We may s......Login to view full explanation

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