From Cutting Planes Algorithms to Compression Schemes and Active Learning

Cutting-plane methods are well-studied localization(and optimization) algorithms. We show that they provide a natural framework to perform machinelearning ---and not just to solve optimization problems posed by machinelearning--- in addition to their intended optimization use. In particular, theyallow one to learn sparse classifiers and provide good compression schemes.Moreover, we show that very little effort is required to turn them intoeffective active learning methods. This last property provides a generic way todesign a whole family of active learning algorithms from existing passivemethods. We present numerical simulations testifying of the relevance ofcutting-plane methods for passive and active learning tasks.Comment: IJCNN 2015, Jul 2015, Killarney, Ireland. 2015, \<http://www.ijcnn.org/\&g

Incremental evolution strategy for function optimization

This paper presents a novel evolutionary approach for function optimization Incremental Evolution Strategy (IES). Two strategies are proposed. One is to evolve the input variables incrementally. The whole evolution consists of several phases and one more variable is focused in each phase. The number of phases is equal to the number of variables in maximum. Each phase is composed of two stages: in the single-variable evolution (SVE) stage, evolution is taken on one independent variable in a series of cutting planes; in the multi-variable evolving (MVE) stage, the initial population is formed by integrating the populations obtained by the SVE and the MVE in the last phase. And the evolution is taken on the incremented variable set. The other strategy is a hybrid of particle swarm optimization (PSO) and evolution strategy (ES). PSO is applied to adjust the cutting planes/hyper-planes (in SVEs/MVEs) while (1+1)-ES is applied to searching optima in the cutting planes/hyper-planes. The results of experiments show that the performance of IES is generally better than that of three other evolutionary algorithms, improved normal GA, PSO and SADE_CERAF, in the sense that IES finds solutions closer to the true optima and with more optimal objective values

Nanoscale Metamaterial Optical Waveguides with Ultrahigh Refractive Indices

We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with numerical simulations based on both metal-dielectric multilayer structures and the effective medium approach. The dependences of waveguide mode indices, propagation lengths and mode areas on different mode orders, free space wavelengths and sizes of waveguide cross sections are studied. Furthermore, waveguide modes are also illustrated with iso-frequency contours in the wave vector space in order to investigate the mechanism of waveguide mode cutoff for high order modes. The deep-subwavelength optical waveguide with a size smaller than {\lambda}0/50 and a mode area in the order of 10-4 {\lambda}02 is realized, and an ultrahigh effective refractive index up to 62.0 is achieved at the telecommunication wavelength. This new type of metamaterial optical waveguide opens up opportunities for various applications in enhanced light-matter interactions.Comment: 22 pages, 8 figure