Haotian Jiang

Haotian Jiang, Qianxiao Li

We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse approximation theorem (Bernstein-type result), which together provide a comprehensive characterization of the types of sequential relationships that can be efficiently captured by a temporal convolutional architecture. The rate estimate improves upon a previous result via the introduction of a refined complexity measure, whereas the inverse approximation theorem is new.

Haotian Jiang, Jian Li, Mingda Qiao

In the Best-$K$ identification problem (Best-$K$-Arm), we are given $N$ stochastic bandit arms with unknown reward distributions. Our goal is to identify the $K$ arms with the largest means with high confidence, by drawing samples from the arms adaptively. This problem is motivated by various practical applications and has attracted considerable attention in the past decade. In this paper, we propose new practical algorithms for the Best-$K$-Arm problem, which have nearly optimal sample complexity bounds (matching the lower bound up to logarithmic factors) and outperform the state-of-the-art algorithms for the Best-$K$-Arm problem (even for $K=1$) in practice.