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.
Improved algorithms for linear stochastic bandits
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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.