Sharp Optimal Algorithm for Derivative-Free Stochastic Convex Optimization in One Dimension

The paper presents an algorithm achieving the optimal convergence rate for one-dimensional derivative-free stochastic convex optimization. The proposed method closes a persistent logarithmic gap between known upper bounds and the lower bound, delivering the first sharp rate guarantee in this setting. The algorithm is computationally efficient and matches the lower bound, addressing a problem where prior approaches fell short even in the simplest one-dimensional case.