Frequency Effects in Decision-Making are Predicted by Dirichlet Probability Distribution Models

AbstractFrequency of reward and average reward value are two types of reward information we utilize when making decisions between two alternative options. Often, these two pieces of information coincide with the highest value option, however, when a slightly less valuable option is presented more frequently, standard reinforcement learning models such as the Delta model can make incorrect predictions. This paper explores the discrepancy in these predictions by way of simulating relevant behavioral tasks with the Delta model, the Decay model, and a novel Bayesian model based on the Dirichlet distribution. We then compare model predictions to behavioral data from some of the same tasks that were simulated. The Delta model provides a poor fit to the data for each of the three presented tasks when compared to the Decay model and the two Bayesian learning models, because it predicts a bias toward options with higher average reward, while the Decay and Bayesian models predict a bias toward reward frequency. The Decay and Bayesian models show a distinct similarity in prediction and fits to the data for most of the tasks. This is because both models predict a bias toward reward frequency rather than average reward magnitude, despite different computational formalisms. However, we also note some interesting discrepancies between the Decay and Bayesian models which will show that in some cases, the frequency of reward may be more important than the reward value.

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