Nonstochastic Multi-Armed Bandits with Graph-Structured Feedback
This addresses the problem of efficient decision-making under partial feedback for scenarios where actions are interrelated, offering a generalization of existing models.
The paper tackles the problem of online learning with partial information, where a decision maker selects actions and observes losses from a subset of related actions, generalizing full-information and bandit settings. It provides algorithms with tight regret bounds based on combinatorial properties of the feedback structure.
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.