Reinforcement learning promises a generic method for adapting agents to arbitrary tasks in arbitrary stochastic environments, but applying it to new real-world problems remains difficult, a few impressive success stories notwithstanding. Most interesting agent-environment systems have large state spaces, so performance depends crucially on efficient generalization from a small amount of experience. Current algorithms rely on model-free function approximation, which estimates the long-term values of states and actions directly from data and assumes that actions have similar values in similar states. This paper proposes model-based function approximation, which combines two forms of generalization by assuming that in addition to having similar values in similar states, actions also have similar effects. For one family of generalization schemes known as averagers, computation of an approximate value function from an approximate model is shown to be equivalent to the computation of the exact value function for a finite model derived from data. This derivation both integrates two independent sources of generalization and permits the extension of model-based techniques developed for finite problems. Preliminary experiments with a novel algorithm, AMBI (Approximate Models Based on Instances), demonstrate that this approach yields faster learning on some standard benchmark problems than many contemporary algorithms.