We obtain minimax lower bounds on the regret for the classical two--armed bandit problem. We provide a finite--sample minimax version of the well--known log "n" asymptotic lower bound of Lai and Robbins. Also, in contrast to the log "n" asymptotic results on the regret, we show that the minimax...

Minimax lower bounds for concept learning state, for example, that for each sample size n and learning rule gn , there exists a distribution of the observation X and a concept C to be learnt such that the expected error of gn is at least a constant times V=n, where V is the vc dimension of the...