A nonlinear relationship between prediction errors and learning rates in human reinforcement-learning

Reinforcement-learning (RL) models have been pivotal to our understanding of how agents perform learning-based adaptions in dynamically changing environments. However, the exact nature of the relationship (e.g., linear, logarithmic etc.) between key components of RL models such as prediction errors (PEs; the difference between the agent's expectation and the actual outcome) and learning rates (a coefficient used by agents to update their beliefs about the environment) has not been studied in detail. Here, across (i) simulations, (ii) reanalyses of readily available datasets and (iii) a novel experiment, we demonstrate that the relationship between PEs and learning rates is (i) nonlinear over the PE/ learning rates space, and (ii) it can be accounted for by an exponential-logarithmic function that can transform the magnitude of PEs instantaneously to learning rates in a novel RL model. In line with the temporal predictions of this model, we show that physiological correlates of learning rates accumulate while learners observe the outcome of their choices and update their beliefs about the environment.