Parameter and model recovery of reinforcement learning models for restless bandit problems

Abstract

Multi-armed restless bandit tasks are regularly applied in psychology and cognitive neuroscience to assess exploration and exploitation behavior in structured environments. These models are also readily applied to examine effects of (virtual) brain lesions on performance, and to infer neurocomputational mechanisms using neuroimaging or pharmacological approaches. However, to infer individual, psychologically meaningful parameters from such data, computational cognitive modeling is typically applied. Recent studies indicate that softmax (SM) decision rule models that include a representation of environmental dynamics (e.g. the Kalman Filter) and additional parameters for modeling exploration and perseveration (Kalman SMEP) fit human bandit task data better than competing models. Parameter and model recovery are two central requirements for computational models: parameter recovery refers to the ability to recover true data-generating parameters; model recovery refers to the ability to correctly identify the true data generating model using model comparison techniques. Here we comprehensively examined parameter and model recovery of the Kalman SMEP model as well as nested model versions, i.e. models without the additional parameters, using simulation and Bayesian inference. Parameter recovery improved with increasing trial numbers, from around .8 for 100 trials to around .93 for 300 trials. Model recovery analyses likewise confirmed acceptable recovery of the Kalman SMEP model. Model recovery was lower for nested Kalman filter models as well as delta rule models with fixed learning rates. Exploratory analyses examined associations of model parameters with model-free performance metrics. Random exploration, captured by the inverse softmax temperature, was associated with lower accuracy and more switches. For the exploration bonus parameter modeling directed exploration, we confirmed an inverse-U-shaped association with accuracy, such that both an excess and a lack of directed exploration reduced accuracy. Taken together, these analyses underline that the Kalman SMEP model fulfills basic requirements of a cognitive model.