The Sense of Confidence during Probabilistic Learning: A Normative Account

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable “feeling of knowing” or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process.Author Summary: Learning is often accompanied by a “feeling of knowing”, a growing sense of confidence in having acquired the relevant information. Here, we formalize this introspective ability, and we evaluate its accuracy and its flexibility in the face of environmental changes that impose a revision of one’s mental model. We evaluate the hypothesis that the brain acts as a statistician that accurately tracks not only the most likely state of the environment, but also the uncertainty associated with its own inferences. We show that subjective confidence ratings varied across successive observations in tight parallel with a mathematical model of an ideal observer performing the optimal inference. Our results suggest that, during learning, the brain constantly keeps track of its own uncertainty, and that subjective confidence may derive from the learning process itself. Our results therefore suggest that subjective confidence, although currently under-explored, could provide key data to better understand learning.