As noted, the gradient vector has both a direction and a magnitude.
Gradient descent algorithms multiply the gradient by a scalar
known as the learning rate (also sometimes called step size)
to determine the next point. For example, if the gradient magnitude is
2.5 and the learning rate is 0.01, then the gradient descent algorithm
will pick the next point 0.025 away from the previous point.

Hyperparameters are the knobs that programmers tweak in machine
learning algorithms. Most machine learning programmers spend a fair
amount of time tuning the learning rate. If you pick a learning rate
that is too small, learning will take too long:

Figure 6. Learning rate is too small.

Conversely, if you specify a learning rate that is too large, the
next point will perpetually bounce haphazardly across the bottom of the well
like a quantum mechanics experiment gone horribly wrong:

Figure 7. Learning rate is too large.

There's a
Goldilocks
learning rate for every regression problem.
The Goldilocks value is related to how flat the loss function is. If you know
the gradient of the loss function is small then you can safely try a larger
learning rate, which compensates for the small gradient and results in a larger
step size.

Figure 8. Learning rate is just right.

Click the plus icon to learn more about the ideal learning rate.

The ideal learning rate in one-dimension is \(\frac{ 1 }{ f(x)'' }\) (the
inverse of the second derivative of f(x) at x).

The ideal learning rate for 2 or more dimensions is
the inverse of the
Hessian (matrix of
second partial derivatives).

The story for general convex functions is more complex.