# On-line Prediction Protocol

The simplest version of the on-line prediction protocol is where Nature outputs observations in the IID fashion. After Forecaster predicts an observation, it is added to the training set, which keeps growing. When each observation `⚠ $z=(x,y)\in\mathbf{Z}=\mathbf{X}\times\mathbf{Y}$`

consists of an object `⚠ $x$`

and its label `⚠ $y$`

, the protocol looks as follows:

`⚠ $n=1,2,\ldots$`

:
`⚠ $y_n$`

A modification is where `⚠ $z_1,z_2,\ldots$`

are coming from an exchangeable probability distribution.

The online prediction protocol is used widely in conformal prediction. There are four important special cases:

(Besides, there are problems of unsupervised learning with the `⚠ $x_n$`

s missing.)