### 2.5 Optional (ungraded) exercises In this part of the exercise, you will get to try out different regularization parameters for the dataset to understand how regularization prevents overfitting. Notice the changes in the decision boundary as you vary $\lambda$. With a small $\lambda$, you should find that the classifier gets almost every training example correct, but draws a very complicated boundary, thus overfitting the data. See the following figures for the decision boundaries you should get for different values of $\lambda$. No regularization (overfitting) ![](https://deepnote.com/publish/780f16d9-24b9-4282-87ef-72b07b12f6f8/file?path=%2FFigures%2Fdecision_boundary3.png) Decision boundary with regularization ![](https://deepnote.com/publish/780f16d9-24b9-4282-87ef-72b07b12f6f8/file?path=%2FFigures%2Fdecision_boundary2.png) Decision boundary with too much regularization ![](https://deepnote.com/publish/780f16d9-24b9-4282-87ef-72b07b12f6f8/file?path=%2FFigures%2Fdecision_boundary4.png) This is not a good decision boundary: for example, it predicts that a point at $x = ( - 0.25, 1.5)$ is accepted $(y = 1)$, which seems to be an incorrect decision given the training set. With a larger $\lambda$, you should see a plot that shows an simpler decision boundary which still separates the positives and negatives fairly well. However, if $\lambda$ is set to too high a value, you will not get a good fit and the decision boundary will not follow the data so well, thus underfitting the data.