  We study the adversarial bandit problem against arbitrary strategies, in
which $S$ is the parameter for the hardness of the problem and this parameter
is not given to the agent. To handle this problem, we adopt the master-base
framework using the online mirror descent method (OMD). We first provide a
master-base algorithm with simple OMD, achieving
$\tilde{O}(S^{1/2}K^{1/3}T^{2/3})$, in which $T^{2/3}$ comes from the variance
of loss estimators. To mitigate the impact of the variance, we propose using
adaptive learning rates for OMD and achieve
$\tilde{O}(\min\{\mathbb{E}[\sqrt{SKT\rho_T(h^\dagger)}],S\sqrt{KT}\})$, where
$\rho_T(h^\dagger)$ is a variance term for loss estimators.
