Hyperparameter tuning is a common practice in the application of machine
learning but is a typically ignored aspect in the literature on
privacy-preserving machine learning due to its negative effect on the overall
privacy parameter. In this paper, we aim to tackle this fundamental yet
challenging problem by providing an effective hyperparameter tuning framework
with differential privacy. The proposed method allows us to adopt a broader
hyperparameter search space and even to perform a grid search over the whole
space, since its privacy loss parameter is independent of the number of
hyperparameter candidates. Interestingly, it instead correlates with the
utility gained from hyperparameter searching, revealing an explicit and
mandatory trade-off between privacy and utility. Theoretically, we show that
its additional privacy loss bound incurred by hyperparameter tuning is
upper-bounded by the squared root of the gained utility. However, we note that
the additional privacy loss bound would empirically scale like a squared root
of the logarithm of the utility term, benefiting from the design of doubling
step.