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：本研究提出了一种针对Hölder连续多元函数的有效全局优化技术。与传统方法构建下界代理函数不同，该算法采用预定的查询生成规则，使其在计算上更具优势。算法性能通过平均或累积遗憾进行评估，该指标同时隐含了简单遗憾的界，并反映了方法的整体有效性。结果表明，在适当参数下，该算法在$n$维空间中优化Hölder指数为$\alpha$的Hölder连续目标函数时，在给定时间范围$T$内达到$O(T^{-\frac{\alpha}{n}})$的平均遗憾界。我们证明该界是极小化最优的。