Complex sentence: Proto-value functions spawns from formulating the problem of value function approximation as approximating real-valued functions on a graph or manifold, which should result in a broader applicability and enables a new class of learning algorithms that learns representations and policies at the same time.
Split into simpler sentences: Proto-value functions arise from reformulating the problem of value function approximation as real-valued function approximation on a graph or manifold. This results in broader applicability of the learned bases and enables a new class of learning algorithms, which learn representations and policies at the same time.