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.

翻译：多元函数的H\"older连续性是一种有效的全局优化技术。与传统方法构造下边界代理函数不同，这种算法采用预定的查询创建规则，使其在计算上优越。该算法的性能是通过平均或累积遗憾度来评估的，遗憾度的上限也反映了该方法的整体有效性。结果表明，在适当的参数下，该算法可以达到一个平均遗憾度界，该界可在给定的时间内优化一个任意H\"older连续目标函数，其中 H\"older指数为$\alpha$，维度为$n$。我们证明，这个界是最小最大的。