that 相当于 the problem。即原句相当于：

The problem of learning is that of choosing from the given set of function...

=The problem of learning is the problem of choosing from the given set of function...

类似用法：

Her status is that of an observer.

=Her status is the status of an observer.

她的身份是观察员。

The only sound is that of knives and forks scraping against china. 

=The only sound is the sound of knives and forks scraping against china.

只听见刀叉摩擦瓷器的刺耳声。

One facet of his role in the film is that of a stern father.

=One facet of his role in the film is the role of a stern father.

他在这部电影中的角色的一个侧面是严厉的父亲。