Data-driven modeling of delay discounting identifies novel discounting behavior

Delay discounting is a preferential choice task that measures the rate at which individuals discount future rewards. Many models that have been proposed for this task fail to describe the full range of behavior that can be exhibited by participants. One reason for this is that most models assume a simple monotonic relationship in which future rewards are discounted as the delay increases. The lack of flexibility of these models can potentially expose experiments to biases introduced by model misspecification. Addressing this problem, we propose a nonparametric Bayesian approach (Gaussian Process with active learning: GPAL), for modeling delay discounting. A Gaussian Process model is fit to data while simultaneously selecting highly informative experimental designs in each trial based on responses from earlier trials. Results show that GPAL is an efficient and reliable framework that is capable of capturing patterns that prominent models are insensitive to. In particular, we identified two of these patterns that were systematically observed in our data and analyze them in detail. These patterns reveal properties that violate common normative assumptions made by virtually all parametric models of discounting and therefore have been rarely discussed in the literature. We offer possible explanations that could account for these abnormal choice behaviors and propose enhancements to existing parametric models motivated by these explanations.