  We present and study a partial-information model of online learning, where a
decision maker repeatedly chooses from a finite set of actions, and observes
some subset of the associated losses. This naturally models several situations
where the losses of different actions are related, and knowing the loss of one
action provides information on the loss of other actions. Moreover, it
generalizes and interpolates between the well studied full-information setting
(where all losses are revealed) and the bandit setting (where only the loss of
the action chosen by the player is revealed). We provide several algorithms
addressing different variants of our setting, and provide tight regret bounds
depending on combinatorial properties of the information feedback structure.
