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

Resilient random modulo cache memories for probabilistically-analyzable real-time systems

Fault tolerance has often been assessed separately in safety-related real-time systems, which may lead to inefficient solutions. Recently, Measurement-Based Probabilistic Timing Analysis (MBPTA) has been proposed to estimate Worst-Case Execution Time (WCET) on high performance hardware. The intrinsic probabilistic nature of MBPTA-commpliant hardware matches perfectly with the random nature of hardware faults. Joint WCET analysis and reliability assessment has been done so far for some MBPTA-compliant designs, but not for the most promising cache design: random modulo. In this paper we perform, for the first time, an assessment of the aging-robustness of random modulo and propose new implementations preserving the key properties of random modulo, a.k.a. low critical path impact, low miss rates and MBPTA compliance, while enhancing reliability in front of aging by achieving a better – yet random – activity distribution across cache sets.Peer ReviewedPostprint (author's final draft

Search for the rare decays B0→J/ψγB^{0}\to J/\psi \gamma and Bs0→J/ψγB^{0}_{s} \to J/\psi \gamma

A search for the rare decay of a $B^{0}$ or $B^{0}_{s}$ meson into the final state $J/\psi\gamma$ is performed, using data collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}=7$ and $8$ TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$. The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than $1.7\times 10^{-6}$ for the $B^{0}\to J/\psi\gamma$ decay mode are excluded at 90% confidence level. For the $B^{0}_{s}\to J/\psi\gamma$ decay mode, branching fraction values larger than $7.4\times 10^{-6}$ are excluded at 90% confidence level, this is the first branching fraction limit for this decay.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-044.htm

Detectability thresholds and optimal algorithms for community structure in dynamic networks

We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated independently at each time step. In this setting (which is a special case of several existing models), we are able to derive the detectability threshold exactly, as a function of the rate of change and the strength of the communities. Below this threshold, we claim that no algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this limit. The first uses belief propagation (BP), which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the BP equations. We verify our analytic and algorithmic results via numerical simulation, and close with a brief discussion of extensions and open questions.Comment: 9 pages, 3 figure