Bayesian active learning with basis functions

A common technique for dealing with the curse of dimensionality in approximate dynamic programming is to use a parametric value function approximation, where the value of being in a state is assumed to be a linear combination of basis functions. Even with this simplification, we face the exploration/exploitation dilemma: an inaccurate approximation may lead to poor decisions, making it necessary to sometimes explore actions that appear to be suboptimal. We propose a Bayesian strategy for active learning with basis functions, based on the knowledge gradient concept from the optimal learning literature. The new method performs well in numerical experiments conducted on an energy storage problem.