Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time to yield novel algorithms in both fields, further motivating the study of their intersection. First, inspired by a recent optimization algorithm that was adaptive to unknown uniform convexity parameters, we present a new active learning algorithm for one-dimensional thresholds that can yield minimax rates by adapting to unknown noise parameters. Next, we show that one can perform $d$-dimensional stochastic minimization of smooth uniformly convex functions when only granted oracle access to noisy gradient signs along any coordinate instead of real-valued gradients, by using a simple randomized coordinate descent procedure where each line search can be solved by $1$-dimensional active learning, provably achieving the same error convergence rate as having the entire real-valued gradient. Combining these two parts yields an algorithm that solves stochastic convex optimization of uniformly convex and smooth functions using only noisy gradient signs by repeatedly performing active learning, achieves optimal rates and is adaptive to all unknown convexity and smoothness parameters.

该论文探讨了近年来关于主动学习和随机凸优化之间的理论相关性，并提出了两种算法，分别适用于一维阈值和d维凸优化的场景，旨在实现对这两个领域的最优控制，支持适应所有未知的凸性和平滑参数。

主动学习与随机凸优化之间的算法联系