AI 中文总结
研究一维无导数随机凸优化问题，提出计算高效算法，实现最优O(1/√T)收敛速度，填补已知上界与下界对数差距，给出该场景下首个精确速率保证。
AI 中文摘要
随机凸优化是一个在一阶反馈下有明确保证的经典问题。相比之下，对于具有噪声函数评估的零阶优化，即使在一维情况下，已知上界与Ω(1/√T)下界之间仍存在对数差距。在这项工作中，我们研究了使用具有次高斯噪声的零阶预言机最小化凸函数f:[0,1]→[0,1]的问题。我们提出了一种计算效率高的算法，实现了最优的O(1/√T)收敛速度，与下界匹配。该结果填补了一维情况下的现有差距，在此设置下提供了第一个精确的速率保证。
英文摘要
Stochastic convex optimization is a classical problem with well-understood guarantees under first-order feedback. In contrast, for zero-order optimization with noisy function evaluations, a logarithmic gap has persisted between known upper bounds and the $Ω(1/\sqrt{T})$ lower bound, even in the one-dimensional case. In this work, we study the problem of minimizing a convex function $f : [0,1] \to [0,1]$ using a zero-order oracle with subGaussian noise. We propose a computationally efficient algorithm that achieves the optimal $O(1/\sqrt{T})$ convergence rate, matching the lower bound. The result closes the existing gap in one dimension, providing the first sharp rate guarantee in this setting.
