Game Of Prediction

A game of prediction is a triple $(\Omega,\Gamma,\lambda)$, where $\Omega$ is an outcome space, $\Gamma$ is a decision space, and $\lambda:\Omega\times\Gamma\to[-\infty,\infty]$ is the loss function. Important special cases are those of:

$$
  \lambda(\omega,\gamma)
  =
  \begin{cases}
    1 & \text{if $\omega\in\gamma$}\\
    0 & \text{otherwise}.
  \end{cases}
$$

The case of region predictions (in particular, interval predictions) is the main object of study in conformal prediction but has never been studied in competitive on-line prediction. This is stated as open problem in the article competitive on-line interval prediction.