Which is this epsilon sub ui,

the error of predicting the user's rating for the item using our scoring function.

We then compute changes or

updates for that items value for the current feature.

And that users value for the current feature.

And these updates are the error times

the other value, so for the item we update using the user value,

for the user we update using the item value.

Minus this additional term that does what we call regularization.

Now we've got two parameters here.

Lambda is our learning rate, which is how fast we want the model to converge.

So if we look at how to do a search,

we are here, we want to look for another value.

We've got our derivative, it tells us to go this way.

How far do we go before we try our estimate again?

That's what the learning rate controls.

If we go too far, then we're going to be really jumpy, and

it's going to be hard to get to the best value, we're going to jump around a lot.

If we go too slow,

then it's going to take us many iterations in order to get to that best value.

So it's kind of a balancing act.