Active sampling with allocation q_j proportional to p_j to the 2/3 achieves tight regret sqrt(n/T) times norm of p to the 2/3 for known context distribution p, with improvement up to Theta(k to the 1/4) over passive sampling.
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Active Context Selection Improves Simple Regret in Contextual Bandits
Active sampling with allocation q_j proportional to p_j to the 2/3 achieves tight regret sqrt(n/T) times norm of p to the 2/3 for known context distribution p, with improvement up to Theta(k to the 1/4) over passive sampling.