Attention includes processes that evaluate stimuli relevance, select the most relevant stimulus against less relevant stimuli, and bias choice behavior toward the selected information. It is not clear how these processes interact. Here, we captured these processes in a reinforcement learning framework applied to a feature-based attention task that required macaques to learn and update the value of stimulus features while ignoring nonrelevant sensory features, locations, and action plans. We found that value-based reinforcement learning mechanisms could account for feature-based attentional selection and choice behavior but required a value-independent stickiness selection process to explain selection errors while at asymptotic behavior. By comparing different reinforcement learning schemes, we found that trial-by-trial selections were best predicted by a model that only represents expected values for the task-relevant feature dimension, with nonrelevant stimulus features and action plans having only a marginal influence on covert selections. These findings show that attentional control subprocesses can be described by (1) the reinforcement learning of feature values within a restricted feature space that excludes irrelevant feature dimensions, (2) a stochastic selection process on feature-specific value representations, and (3) value-independent stickiness toward previous feature selections akin to perseveration in the motor domain. We speculate that these three mechanisms are implemented by distinct but interacting brain circuits and that the proposed formal account of feature-based stimulus selection will be important to understand how attentional subprocesses are implemented in primate brain networks.