Beyond square-root regret guarantees for FTPL

Establish whether Follow-the-Perturbed-Leader algorithms for adversarial linear bandits can achieve first-order, second-order, or best-of-both-worlds regret guarantees.

Background

The presented FTPL method provides a worst-case square-root regret guarantee, but the explicit spanner exploration used by the algorithm incurs an exploration cost that is itself of square-root order in the horizon. The paper leaves unresolved whether FTPL can attain stronger adaptive guarantees, including first-order, second-order, or best-of-both-worlds regret bounds.