Perceptron Update $1$

$0/1$ point $($graded$)$

Now consider the Perceptron algorithm with Offset. Whenever there is a "mistake" $($or equivalently, whenever i$.$e$.$ when the label and do not match$),$ perceptron updates

and

More formally, the Perceptron Algorithm with Offset is defined as follows:

Perceptron

$$initialize $($vector$)$; $($scalar$)$

$$for do

$$for do

$$if then

$$update

$$update

In the next set of problems, we will try to understand why such an update is a reasonable one.

When a mistake is spotted, do the updated values of and provide a better prediction? In other words, is

always greater than or equal to