Adaptivity in linear bandits for ε-best arm identification gives only logarithmic improvements on hypercube, ℓ2 ball, m-sets and multi-task settings but polynomial-factor gains on a specially constructed action set, enabled by an adaptive O(d log(1/δ)/ε²) ℓ2-norm estimator.
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On the Power of Adaptivity for $\varepsilon$-Best Arm Identification in Linear Bandits
Adaptivity in linear bandits for ε-best arm identification gives only logarithmic improvements on hypercube, ℓ2 ball, m-sets and multi-task settings but polynomial-factor gains on a specially constructed action set, enabled by an adaptive O(d log(1/δ)/ε²) ℓ2-norm estimator.