Tuning bandit algorithms in stochastic environments

International audienceAlgorithms based on upper-confidence bounds for balancing exploration and exploitation are gaining popularity since they are easy to implement, efficient and effective. In this paper we consider a variant of the basic algorithm for the stochastic, multi-armed bandit problem that takes into account the empirical variance of the different arms. In earlier experimental works, such algorithms were found to outperform the competing algorithms. The purpose of this paper is to provide a theoretical explanation of these findings and provide theoretical guidelines for the tuning of the parameters of these algorithms. For this we analyze the expected regret and for the first time the concentration of the regret. The analysis of the expected regret shows that variance estimates can be especially advantageous when the payoffs of suboptimal arms have low variance. The risk analysis, rather unexpectedly, reveals that except for some very special bandit problems, the regret, for upper confidence bounds based algorithms with standard bias sequences, concentrates only at a polynomial rate. Hence, although these algorithms achieve logarithmic expected regret rates, they seem less attractive when the risk of suffering much worse than logarithmic regret is also taken into account

Electronic and Structural Properties of a 4d-Perovskite: Cubic Phase of SrZrO3_3

First-principles density functional calculations are performed within the local density approximation to study the electronic properties of SrZrO$_3$, an insulating 4d-perovskite, in its high-temperature cubic phase, above 1400 K, as well as the generic 3d-perovskite SrTiO$_3$, which is also a d^0-insulator and cubic above 105 K, for comparison reasons. The energy bands, density of states and charge density distributions are obtained and a detailed comparison between their band structures is presented. The results are discussed also in terms of the existing data in the literature for both oxides.Comment: 5 pages, 2 figure

The influence of codoping on optical properties and glass connectivity of silica fiber preforms

International audienceRare Earth Elements-doped glasses have applications in many fields, and for example, Al and Ce codoping in silica optical fibers is usually done to attenuate the optical degradation (photodarkening) of, e.g. Yb and Tm doped silica optical fibers. To shed some light on the effect of codoping on the optical properties and the glass structure of SiO 2 fibers, we investigated a SiO 2 fiber preform having a gradual increase of the CeO 2 + Al 2 O 3 content from 1.5 to 6.3 mol% and a CeO 2 /Al 2 O 3 molar ratio varying from 0.04 to 1.4. Raman and photo-luminescence spectroscopies have been used to evaluate changes in the short-and medium-range order both in the cladding and in the core portions, and the evolution of the glass optical properties, respectively. The variations of the excitation and emission have been linked to modifications in the vibration bands of the Raman spectra, and in turn, the relationship between optical properties and glass connectivity has been carefully considered. Our results show that there is a strong positive linear relationship between the increase of the Raman bands in the high-frequency range and the red-shift of the excitation maxima. Therefore, the change of distances and bond covalency character influences, in the same way, both the photoluminescence behavior of the core and the connectivity of the amorphous network

Evidence of polyamorphic transitions during densified SiO2 glass annealing

International audienceIn situ X-ray scattering monitoring is carried out during temperature annealing on different densified SiO2 glasses. Density fluctuations and intermediate range coherence from X-ray scattering (small-angle X-ray scattering) and diffraction (wide angle X-ray scattering) evidence a maximum in their evolution at the same relaxation time. These extrema confirm the existence of an intermediate transitory disordered state between the two more ordered high and low density amorphous states. We propose that the existence of this transitory state confirms the existence of two mega basins in the energy landscape and therefore an amorphous-amorphous transition. Including older Raman results, we show that this intermediate disorder state implies similar mechanisms at all length scales from a few angstroms to 5 nm

Devitrification Behavior of Sol-Gel Derived ZrO2-SiO2 Rare-Earth Doped Glasses: Correlation between Structural and Optical Properties

Optical and structural properties of glasses and glass-ceramics (GC) obtained by different heat-treatment of Tb and Tb-Yb doped sol-gel derived 30ZrO2-70SiO2 materials were investigated. A glass was formed after treatment at 700 °C whereas devitrification of the media after the treatment at 1000 and 1100 °C, led to the formation of GC containing up to three different crystalline phases, namely, tetragonal ZrO2, Yb-disilicate and cristobalite. The modification of the optical properties through the heat treatment was caused by redistribution of the rare earth elements (REE) among the different phases: both Tb and Yb entered the t-ZrO2 lattice, Yb can also be present in the form of a Yb2Si2O7 crystal. Devitrification led to an increase in Tb→Yb energy transfer efficiency as compared to the glass, though it was higher in the samples heat-treated at 1000 °C than in those treated at 1100 °C. The most intensive Yb3+ luminescence, induced by the energy transfer from the Tb3+ ion, was observed at the interface between t-ZrO2 and the glassy phases, due to the high concentration of REE in this area caused by the inability of ZrO2 to accept larger amounts of the REE. The mechanisms of the Tb→Yb energy transfer vary between different phases of the GC. The results obtained in this study are important for the development of spectral down-converters for potential solar energy applications based on Tb-Yb co-doped glass-ceramics