GATE 2026 DA – Question 29
Consider that for a supervised learning task, the objective function being minimized is $f_w(x) = wx$, where $x \in \mathbb{R}$ is the input and $w \in \mathbb{R}$ is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates.
Suppose that at the end of iteration $i$, the value of $w$ becomes 10.00.
Let $x = 10.00$ be the input for iteration $(i + 1)$.
The value of $w$ at the end of iteration $(i + 1)$ is __________ . (*Rounded off to two decimal places*)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 8.96 to 9.04
Explanation
The gradient of $f_w(x) = wx$ with respect to $w$ is $x = 10$. One stochastic gradient descent step gives $w_{new} = w - \eta\frac{\partial f}{\partial w} = 10.00 - 0.10 \times 10.00 = 9.00$.