Update: we recently discovered the performative prediction (Perdomo et al., 2020) literature (HT Alex Pan). This is a machine learning setting where we choose a model parameter (e.g., parameters for a neural network) that minimizes expected loss (e.g., classification error). In performative prediction, the distribution over data points can depend on the choice of model parameter. Our setting is thus a special case in which the parameter of interest is a probability distribution, the loss is a scoring function, and data points are discrete outcomes. Most results in this post have analogues in performative prediction. We will give a more detailed comparison in an upcoming paper. We also discuss performative prediction more in our follow-up post on stop-gradients.
Update: we recently discovered the performative prediction (Perdomo et al., 2020) literature (HT Alex Pan). This is a machine learning setting where we choose a model parameter (e.g., parameters for a neural network) that minimizes expected loss (e.g., classification error). In performative prediction, the distribution over data points can depend on the choice of model parameter. Our setting is thus a special case in which the parameter of interest is a probability distribution, the loss is a scoring function, and data points are discrete outcomes. Most results in this post have analogues in performative prediction. We will give a more detailed comparison in an upcoming paper. We also discuss performative prediction more in our follow-up post on stop-gradients.