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ml-recall

#steepest-descent

3 questions from Optimization & Calculus, Training Deep Networks

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3 questions · 3 min · score and explanations at the end

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Question 1: Short answer

mediumAI-checkedOptimization & Calculus

Steepest descent under the max norm solves Δw⋆=arg min⁡Δw[g⊤Δw+λ2∥Δw∥∞2]\Delta w^\star = \operatorname*{arg\,min}_{\Delta w}\Big[g^\top \Delta w + \tfrac{\lambda}{2}\lVert \Delta w \rVert_\infty^2\Big] and the solution is Δw⋆=−∥g∥1λ sign(g)\Delta w^\star = -\frac{\lVert g \rVert_1}{\lambda}\,\mathrm{sign}(g). For g=(3,−1,0.5)g = (3, -1, 0.5) and λ=2\lambda = 2, what is the second component Δw2⋆\Delta w^\star_2?

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