First-order regret bounds for combinatorial semi-bandits

We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making each decision, the learner observes the losses associated with its action, but not other losses. For this problem, there are several learning algorithms that guarantee that the learner's expected regret grows as $\widetilde{O}(\sqrt{T})$ with the number of rounds $T$. In this paper, we propose an algorithm that improves this scaling to $\widetilde{O}(\sqrt{{L_T^*}})$, where $L_T^*$ is the total loss of the best action. Our algorithm is among the first to achieve such guarantees in a partial-feedback scheme, and the first one to do so in a combinatorial setting.Comment: To appear at COLT 201

Photophysics of single silicon vacancy centers in diamond: implications for single photon emission

Single silicon vacancy (SiV) color centers in diamond have recently shown the ability for high brightness, narrow bandwidth, room temperature single photon emission. This work develops a model describing the three level population dynamics of single SiV centers in diamond nanocrystals on iridium surfaces including an intensity dependent de-shelving process. Furthermore, we investigate the brightness and photostability of single centers and find maximum single photon rates of 6.2 Mcps under continuous excitation. We investigate the collection efficiency of the fluorescence and estimate quantum efficiencies of the SiV centers.Comment: 15 pages, 7 figures, version 2 accepted for publication in Optics Expres

Adjustment in the textile and clothing industry: The case of West Germany

Among the industries expected in future to be - according to several surveys - exposed to high pressure through adjustment: requirements due to accelerating export performance by developing countries, the textile and clothing industry occupies a predominant rank. The question whether developing countries are well advised to penetrate into the markets of developed countries as new suppliers of textile and clothing products has subsequently led to vehement controversies. The following contribution does not intend to examine more closely the questions raised in this connection, but, within the limits of this contribution, the following aspects shall be treated: - extent and direction of the structural change in the textile and clothing industry of the Federal Republic of Germany during the last decade, and their origin; - to show the protective measures granted to the West German producers of textile and clothing goods vis-a-vis their competitors from so - called low price countries and to analyse the quantitative, effects of these protective measures; - to examine the question which percentage of the imports from so-called low price countries is absorbed by the different industrial countries and whether it is possible to develop standards for a fair distribution of the import burden from low price countries; - finally to analyse more closely the development of textile and clothing exports from developing and so-called low price countries, in order to obtain possibly data about the future development.

Explore no more: Improved high-probability regret bounds for non-stochastic bandits

This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them requires a large deal of technical effort and significant modifications to the standard, more intuitive algorithms that come only with guarantees that hold on expectation. One of these modifications is forcing the learner to sample arms from the uniform distribution at least $\Omega(\sqrt{T})$ times over $T$ rounds, which can adversely affect performance if many of the arms are suboptimal. While it is widely conjectured that this property is essential for proving high-probability regret bounds, we show in this paper that it is possible to achieve such strong results without this undesirable exploration component. Our result relies on a simple and intuitive loss-estimation strategy called Implicit eXploration (IX) that allows a remarkably clean analysis. To demonstrate the flexibility of our technique, we derive several improved high-probability bounds for various extensions of the standard multi-armed bandit framework. Finally, we conduct a simple experiment that illustrates the robustness of our implicit exploration technique.Comment: To appear at NIPS 201