Stable Function Approximation in Dynamic Programming

The success of reinforcement learning in practical problems depends on the ability to combine function approximation with temporal di erence methods such as value iteration. Experiments in this area have produced mixed results; there have been both notable successes and notable disappointments. Theory has been scarce, mostly due to the difculty of reasoning about function approximators that generalize beyond the observed data. We provide a proof of convergence for a wide class of temporal di erence methods involving function approximators such as k-nearest-neighbor, and show experimentally that these methods can be useful. The proof is based on a view of function approximators as expansion or contraction mappings. In addition, we present a novel view of tted value iteration: an approximate algorithm for one environment turns out to be an exact algorithm for a di erent environment.