  This study presents an effective global optimization technique designed for
multivariate functions that are H\"older continuous. Unlike traditional methods
that construct lower bounding proxy functions, this algorithm employs a
predetermined query creation rule that makes it computationally superior. The
algorithm's performance is assessed using the average or cumulative regret,
which also implies a bound for the simple regret and reflects the overall
effectiveness of the approach. The results show that with appropriate
parameters the algorithm attains an average regret bound of
$O(T^{-\frac{\alpha}{n}})$ for optimizing a H\"older continuous target function
with H\"older exponent $\alpha$ in an $n$-dimensional space within a given time
horizon $T$. We demonstrate that this bound is minimax optimal.
