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

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

An Astronomical Account: A History of Hatter Planetarium from 1966-2006

When most individuals stare up at the vast dome of Hatter Planetarium, they often gaze upon the projected stars appearing on its surface, listening to an astronomical story told by one of its operators. However, there is a second story told by the planetarium itself. This story is the history of Hatter Planetarium, which spans five decades and includes the events in the lives of several individuals who have played a critical role in its existence at Gettysburg College. Its history has encompassed several phases of Gettysburg College traditions but is in danger of passing permanently and fixedly into the history books. Gettysburg College’s Hatter Planetarium is an example of a facility, rich in history, which has come to represent a steadfast bond between community and campus relations. [excerpt] Course Information: Course Title: HIST 300: Historical Method Academic Term: Spring 2006 Course Instructor: Dr. Michael J. Birkner \u2772 Hidden in Plain Sight is a collection of student papers on objects that are hidden in plain sight around the Gettysburg College campus. Topics range from the Glatfelter Hall gargoyles to the statue of Eisenhower and from historical markers to athletic accomplishments. You can download the paper in pdf format and click View Photo to see the image in greater detail.https://cupola.gettysburg.edu/hiddenpapers/1021/thumbnail.jp

Kinetics of helium bubble formation in nuclear materials

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by a discrete kinetic equations for the number densities of bubbles having $k$ atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.Comment: 24 pages, 6 figures, to appear in Physica

Relaxation dynamics of multi-level tunneling systems

A quantum mechanical treatment of an asymmetric double-well potential (DWP) interacting with a heat bath is presented for circumstances where the contribution of higher vibrational levels to the relaxation dynamics cannot be excluded from consideration. The deep quantum limit characterized by a discrete energy spectrum near the barrier top is considered. The investigation is motivated by simulations on a computer glass which show that the considered parameter regime is ``typical'' for DWPs being responsible for the relaxation peak of sound absorption in glasses. Relaxation dynamics resembling the spatial- and energy-diffusion-controlled limit of the classical Kramers' problem, and Arrhenius-like behavior is found under specific conditions.Comment: 23 pages, RevTex, 2 figures can be received from the Authors upon reques

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