Convergence of Online Mirror Descent

In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the step size sequence $\{\eta_t\}_{t}$ for the convergence of an OMD algorithm with respect to the expected Bregman distance induced by the mirror map. The condition is $\lim_{t\to\infty}\eta_t=0, \sum_{t=1}^{\infty}\eta_t=\infty$ in the case of positive variances. It is reduced to $\sum_{t=1}^{\infty}\eta_t=\infty$ in the case of zero variances for which the linear convergence may be achieved by taking a constant step size sequence. A sufficient condition on the almost sure convergence is also given. We establish tight error bounds under mild conditions on the mirror map, the loss function, and the regularizer. Our results are achieved by some novel analysis on the one-step progress of the OMD algorithm using smoothness and strong convexity of the mirror map and the loss function.Comment: Published in Applied and Computational Harmonic Analysis, 202

Technology, Innovation and Latecomer Strategies: Evidence from the Mobile Handset Manufacturing Sector in China

Since the entry of Chinese domestic mobile handset manufacturers in 1998, Chinese domestic suppliers have successfully surpassed the market share of joint ventures (JVs) while direct imports have been largely phased out. By examining China’s mobile handset manufacturing sector as a whole and through case studies, we found several factors that contributed to the success of China’s domestic handset manufacturers which can be classified into three categories: market conditions, competition, and government’s support.

Estimating the effect of semi-transparent low-height road traffic noise barriers with ultra weak variational formulation

The ultra weak variational formulation (UWVF) approach is used to study the effect of semi-transparent road traffic noise barriers of limited height. This numerical method is extended to simulate sound propagation through a porous medium, based on the Zwicker and Kosten phenomenological porous rigid-frame model. An efficient approach to calculate noise levels in multi-lane road traffic noise situations is presented. The UWVF method was validated successfully by comparison with finite-difference time-domain (FDTD) calculations, for the case of sound propagation near a porous, low-height, and complex shaped noise barrier, and for sound propagation above porous ground in a refracting atmosphere. An assessment is made of the shielding of various porous low-height noise barriers for people on the pavement along the road. Porous barriers were shown to improve noise shielding when compared to geometrically identical rigid noise barriers