Before revision:  We show that, when the context vectors are adversarially chosen in d-dimensional linear contextual bandits, the learner needs \Omega (d \log T/ \log ( d \log T) ) policy switches to achieve the minimax-optimal expected regret, almost matching the O(d \log T) upper bound by Abbasi-Yadkori et al. 2011(\log d, \log \log T) factors} ;
After revision:  We show that, when the context vectors are adversarially chosen in d-dimensional linear contextual bandits, the learner needs \Omega (d \log T/ \log ( d \log T) ) policy switches to achieve the minimax-optimal expected regret, almost matching the O(d \log T) upper bound by Abbasi-Yadkori et al. regret, and this is optimal up to \mathrm{poly(\log d, \log \log T) factors} ;