How the Kernel Perceptron Algorithm Works: The Update

$1$ point possible $($graded$)$

As in the previous problem, our goal is to correctly reformulate the original perceptron algorithm. In other words, we want the algorithm to be about updating $\text{'}$s instead of $.$

Kernel Perceptron

$$initialize to some values;

$$for

$$for

$$if

$$Update appropriately

Now look at the line "Update appropriately" in the above algorithm. Remember that we express as

Assuming that there was a mistake in classifying the th data point i$.$e$.$

which of the following conditions about is equivalent to

the update condition of the original algorithm?