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Deep Learning · Quiz 2 · 16 Mar 2025 · January 2025 term

Question 13: Consider a loss function, L(w) = w^3 + 2w, where w repre…

Question 13

+1 markNumerical answer

Consider a loss function, L(w)=w3+2wL(w) = w^3 + 2w, where ww represents the model parameter. The AdaGrad optimizer is used to minimize this loss. The learning rate η\eta is set to 0.50.5, and at the initial iteration (t=0t = 0), the parameter ww has a starting value of w0=2w_0 = 2.

AdaGrad Update Rule:

vt=vt−1+(∇wt)2wt+1=wt−ηvt+ϵ∗∇wtv−1=0use ϵ=0\begin{aligned} v_t &= v_{t-1} + (\nabla w_t)^2 \\ w_{t+1} &= w_t - \frac{\eta}{\sqrt{v_t + \epsilon}} * \nabla w_t \\ v_{-1} &= 0 \\ \text{use } \epsilon &= 0 \end{aligned}

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Correct answer: 8.75 (accepted within ±0.15)

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Question 13 of 23 in the IIT Madras BS Deep Learning (Deep Learning) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term (IIT M DEGREE AN EXAM QDB2 16 Mar 2025). It carries 1 mark.

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