In order for an autonomous agent to behave robustly in a variety of environments, it must have the ability to learn approximations to many different functions. The function approximator used by such an agent is subject to a number of constraints that may not apply in a traditional supervised learning setting. Many different function approximators exist and are appropriate for different problems. This paper proposes a set of criteria for function approximators for autonomous agents. Additionally, for those problems on which polynomial regression is a candidate technique, the paper presents an enhancement that meets these criteria. In particular, using polynomial regression typically requires a manual choice of the polynomial’s degree, trading off between function accuracy and computational and memory efficiency. Polynomial Regression with Automated Degree (PRAD) is a novel function approximation method that uses training data to automatically identify an appropriate degree for the...