论文标题
Lipschitz连续多元函数的有效最小最佳全局优化
Efficient Minimax Optimal Global Optimization of Lipschitz Continuous Multivariate Functions
论文作者
论文摘要
在这项工作中，我们提出了一种有效的最小值最佳全局优化算法，用于多变量Lipschitz连续函数。为了评估我们的方法的性能，我们利用了平均遗憾，而不是传统的简单遗憾，正如我们所表明的那样，由于问题本身的固有硬度，因此我们不适合在多元非convex优化中使用。由于我们研究了算法的平均遗憾，因此我们的结果也直接暗示了简单的遗憾。我们的方法没有构建下限代理函数，而是利用预定的查询创建规则，这使其在计算上优于piyavskii-shubert变体。我们表明，我们的算法达到了$ O（l \ sqrt {n} t^{ - \ frac {1} {n}}} $的平均遗憾，以优化$ n $ n $ -dimensional $ l $ -lipschitz的持续目标，以$ t $ t $ t $ t $ t $ t $，我们显示出最大的time time horve time time time horve optal，comax optal conmax optal at in Minamax。
In this work, we propose an efficient minimax optimal global optimization algorithm for multivariate Lipschitz continuous functions. To evaluate the performance of our approach, we utilize the average regret instead of the traditional simple regret, which, as we show, is not suitable for use in the multivariate non-convex optimization because of the inherent hardness of the problem itself. Since we study the average regret of the algorithm, our results directly imply a bound for the simple regret as well. Instead of constructing lower bounding proxy functions, our method utilizes a predetermined query creation rule, which makes it computationally superior to the Piyavskii-Shubert variants. We show that our algorithm achieves an average regret bound of $O(L\sqrt{n}T^{-\frac{1}{n}})$ for the optimization of an $n$-dimensional $L$-Lipschitz continuous objective in a time horizon $T$, which we show to be minimax optimal.
