TRAiL, a tangential forced-exploration algorithm for linear bandits, achieves Omega(sqrt(T)) inference quality and O(sqrt(T) log T) regret with high probability, and a new lower bound shows regret and inference quality must trade off.
On the Minimax Regret for Linear Bandits in a wide variety of Action Spaces
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abstract
As noted in the works of \cite{lattimore2020bandit}, it has been mentioned that it is an open problem to characterize the minimax regret of linear bandits in a wide variety of action spaces. In this article we present an optimal regret lower bound for a wide class of convex action spaces.
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Tangential Randomization in Linear Bandits (TRAiL): Guaranteed Inference and Regret Bounds
TRAiL, a tangential forced-exploration algorithm for linear bandits, achieves Omega(sqrt(T)) inference quality and O(sqrt(T) log T) regret with high probability, and a new lower bound shows regret and inference quality must trade off.