# PAC learning definition and the properties of the problem

I am trying to understand the basic definition of realizable PAC learning from Shai Shalev-Shwartz's "understanding machine learning". They define a hypothesis class H to be PAC learnable if for every distribution D over the instances, and for any labeling function f, an approximately correct hypothesis can be learned with high probability over the random choice of a training set.

An issue that is not entirely clear ot me: they define PAC learnability as a property of an hypothesis class, i.e., of a solution. Intuitively I'd expect that learnability would be a property of the problem, as some problems are harder than others. What role do the properties of the problem play in the definition?

For example, if you want to find the best SVM to classify your data, your hypothesis class is given exactly by a set of weights $w$ and biases $b$. The fact that you try to maximize the margin is reflected only in the fact that this will give you a good generalization bound later on. But this works only because SVMs are a relatively simple class.