Contextual bandits with general function approximation can achieve regret scaling with cumulative reward variance and only logarithmically with the reward range, using Catoni robust mean estimators, with a matching lower bound for the leading term.
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Catoni Contextual Bandits are Robust to Heavy-tailed Rewards
Contextual bandits with general function approximation can achieve regret scaling with cumulative reward variance and only logarithmically with the reward range, using Catoni robust mean estimators, with a matching lower bound for the leading term.