Step 1: Understanding the learning types.
In supervised learning, the agent is given input-output pairs, where the output is labeled. The agent then learns a function that maps inputs to outputs.
Step 2: Analysis of options.
- (A) Supervised: Correct, in supervised learning, input-output pairs are used to train the model.
- (B) Unsupervised: Incorrect, in unsupervised learning, there are no output labels provided.
- (C) Reinforcement: Incorrect, reinforcement learning involves agents interacting with an environment and learning through rewards or punishments.
- (D) Semi-supervised: Incorrect, semi-supervised learning involves both labeled and unlabeled data.
Step 3: Conclusion.
The correct answer is (A) Supervised.
Consider designing a linear classifier
\[ y = \text{sign}(f(x; w, b)), \quad f(x; w, b) = w^T x + b \]on a dataset \( D = \{(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)\} \), where \( x_i \in \mathbb{R}^d \), \( y_i \in \{+1, -1\} \), for \( i = 1, 2, \dots, N \).
Recall that the sign function outputs \( +1 \) if the argument is positive, and \( -1 \) if the argument is non-positive. The parameters \( w \) and \( b \) are updated as per the following training algorithm:
\[ w_{\text{new}} = w_{\text{old}} + y_n x_n, \quad b_{\text{new}} = b_{\text{old}} + y_n \]whenever \( \text{sign}(f(x_n; w_{\text{old}}, b_{\text{old}})) \neq y_n \).
In other words, whenever the classifier wrongly predicts a sample \( (x_n, y_n) \) from the dataset, \( w_{\text{old}} \) gets updated to \( w_{\text{new}} \), and likewise \( b_{\text{old}} \) gets updated to \( b_{\text{new}} \).
Consider the case \( (x_n, +1) \), where \( f(x_n; w_{\text{old}}, b_{\text{old}}) < 0 \). Then:
Consider the neural network shown in the figure with \[ \text{inputs: } u = 2, \, v = 3 \] \[ \text{weights: } a = 1, b = 1, c = 1, d = -1, e = 4, f = -1 \] \[ \text{output: } y \] R denotes the ReLU function, \( R(x) = \max(0, x) \).

Given \( u = 2, v = 3, a = 1, b = 1, c = 1, d = -1, e = 4, f = -1 \), which one of the following is correct?