From Bandits to Experts: A Tale of Domination and Independence
This work addresses a theoretical problem in multi-armed bandits for researchers, providing incremental insights into regret bounds and algorithm efficiency.
The paper tackles the problem of regret characterization in the partial observability model for multi-armed bandits, showing that regret can be characterized by dominating and independence numbers of the observability graph, and that optimal regret is achievable without prior graph access in the undirected case.
We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner can achieve optimal regret without even accessing the observability graph before selecting an action. Both results are shown using variants of the Exp3 algorithm operating on the observability graph in a time-efficient manner.