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Mock Exam 2018 - Multiple Choice - Regularization

Hello, here is a Multiple Choice Question and its solution

We add a regularization term because

  1. this sometimes renders the minimization problem of the cost function into a strictly convex/concave
    problem
  2. this tends to avoid overfitting
  3. this converts a regression problem into a classification problem
    Solution: 1 and 2 are correct

I find the above 1. answer counter-intuitive as the purpose of regularization is purely to fight overfitting...
When have we seen that adding a regularization term renders the problem into a strictly convex/concave problem ?

Thank you in advance for your help

Following up on my own question...

I guess the explanation for this is the case of the logistic regression on linearly separable data, for which the weights will converge to infinity (which means the optimum is infinity, which means the function is not strictly convex (there are many infinities)) .
Regularization makes sure we converge to a finite solution, which somehow is unique ?

Well confused over this...

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