GATE 2026 DA Q.29: solution and answer

Official answer: 8.90 to 9.10Source: Official answer key, GATE 2026 DA (IIT Guwahati)

1. The objective is $f_w(x)=wx$, which is linear in the parameter $w$. Stochastic gradient descent updates $w$ using the gradient of this objective with respect to $w$ for the current sample.

2. Differentiate with respect to $w$, treating $x$ as a constant: $\frac{\partial f_w(x)}{\partial w}=x$.

3. At iteration $(i+1)$ the input is $x=10.00$, so the gradient is $10.00$. The value $w=10.00$ from the end of iteration $i$ does not enter the gradient, because the objective is linear in $w$.

4. SGD update rule: $w_{\text{new}}=w_{\text{old}}-\eta \frac{\partial f}{\partial w}$ with $\eta =0.10$ and $w_{\text{old}}=10.00$.

5. Substitute: $w_{\text{new}}=10.00-0.10\times 10.00=10.00-1.00=9.00$.