Overfitting occurs when a model learns the training data too well, including its inherent noise, which leads to poor generalization on unseen data. Evaluating the provided options for preventing this:
Option A is a good practice: Using a two-part cost function that includes a regularizer explicitly penalizes model complexity. By adding this penalty (such as $L_1$ or $L_2$ regularization) to the training error, the model is forced to learn simpler, smoother patterns rather than contorting to fit every noisy data point.
Option B is not a good practice: Relying solely on an optimizer to minimize error specifically on the training data is the primary cause of overfitting. Without constraints, driving the training error perfectly to zero almost guarantees the model will perform poorly on new data.
Option C is a good practice: This describes a strategy incorporating Structural Risk Minimization and early stopping based on cross-validation. By monitoring performance on a separate validation set and stopping the training process as soon as the cross-validation error starts to increase, you halt the model right before it begins memorizing the training data at the expense of generalization.
Option D is not a good practice: Randomly discarding 50% of your samples reduces the amount of information the model has available to learn the true underlying distribution. Less training data generally increases the model's variance and makes it much more susceptible to overfitting the remaining small subset.
Therefore, the correct options are A and C.
