Yijun Huang

Jie Zhong, Yijun Huang, Ji Liu

This paper considers the multi-armed thresholding bandit problem -- identifying all arms whose expected rewards are above a predefined threshold via as few pulls (or rounds) as possible -- proposed by Locatelli et al. [2016] recently. Although the proposed algorithm in Locatelli et al. [2016] achieves the optimal round complexity in a certain sense, there still remain unsolved issues. This paper proposes an asynchronous parallel thresholding algorithm and its parameter-free version to improve the efficiency and the applicability. On one hand, the proposed two algorithms use the empirical variance to guide the pull decision at each round, and significantly improve the round complexity of the "optimal" algorithm when all arms have bounded high order moments. The proposed algorithms can be proven to be optimal. On the other hand, most bandit algorithms assume that the reward can be observed immediately after the pull or the next decision would not be made before all rewards are observed. Our proposed asynchronous parallel algorithms allow making the choice of the next pull with unobserved rewards from earlier pulls, which avoids such an unrealistic assumption and significantly improves the identification process. Our theoretical analysis justifies the effectiveness and the efficiency of proposed asynchronous parallel algorithms.

Yijun Huang, Ji Liu

Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the nonzeros \emph{evenly} distributed in different groups. The exclusive sparsity norm has been widely used to serve to this purpose. However, it still lacks systematical studies for exclusive sparsity norm optimization. This paper offers two main contributions from the optimization perspective: 1) We provide several efficient algorithms to solve exclusive sparsity norm minimization with either smooth loss or hinge loss (non-smooth loss). All algorithms achieve the optimal convergence rate $O(1/k^2)$ ($k$ is the iteration number). To the best of our knowledge, this is the first time to guarantee such convergence rate for the general exclusive sparsity norm minimization; 2) When the group information is unavailable to define the exclusive sparsity norm, we propose to use the random grouping scheme to construct groups and prove that if the number of groups is appropriately chosen, the nonzeros (true features) would be grouped in the ideal way with high probability. Empirical studies validate the efficiency of proposed algorithms, and the effectiveness of random grouping scheme on the proposed exclusive SVM formulation.

Xiangru Lian, Yijun Huang, Yuncheng Li et al.

Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and speedup properties, mainly due to the nonconvexity of most deep learning formulations and the asynchronous parallel mechanism. To fill the gaps in theory and provide theoretical supports, this paper studies two asynchronous parallel implementations of SG: one is on the computer network and the other is on the shared memory system. We establish an ergodic convergence rate $O(1/\sqrt{K})$ for both algorithms and prove that the linear speedup is achievable if the number of workers is bounded by $\sqrt{K}$ ($K$ is the total number of iterations). Our results generalize and improve existing analysis for convex minimization.