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Let the L2 regularized logistic regression function is given by, \begin{align} f(w) &= \frac{1}{N} \sum_i \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2 \ = \frac{1}{N} \sum_i f_i(w), \end{align} where $t_i \in \mathbb{R}$, $w, x_i \in \mathbb{R}^n$, $\mu \in \mathbb{R}$, and $f_i(w) := \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2$ .

Questions:

  • How would/could I find the (small) Lipschitz constant $M$ and $\nu$-strongly parameter of $f(w)$?
  • How can I find the (small) Lipschitz constant $L$ of $\nabla f(w)$ and $L_i$ of $\nabla f_i(w)$?

I am sorry if this question has already been asked or it is trivial to compute (analytically?).

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