Stochastic Bandits with Delay-Dependent Payoffs

Motivated by recommendation problems in music streaming platforms, we propose a nonstationary stochastic bandit model in which the expected reward of an arm depends on the number of rounds that have passed since the arm was last pulled. After proving that finding an optimal policy is NP-hard even when all model parameters are known, we introduce a class of ranking policies provably approximating, to within a constant factor, the expected reward of the optimal policy. We show an algorithm whose regret with respect to the best ranking policy is bounded by Oe 1a kT , where k is the number of arms and T is time. Our algorithm uses only O k ln ln T) switches, which helps when switching between policies is costly. As constructing the class of learning policies requires ordering the arms according to their expectations, we also bound the number of pulls required to do so. Finally, we run experiments to compare our algorithm against UCB on different problem instance

Association between the multidimensional prognostic index and mortality during 15 Years of Follow-up in the InCHIANTI Study

Background: Multidimensional Prognostic Index (MPI) is recognized as a prognostic tool in hospitalized patients, but data on the value of MPI in community-dwelling older persons are limited. Using data from a representative cohort of community-dwelling persons, we tested the hypothesis that MPI explains mortality during 15 years of follow-up. Methods: A standardized comprehensive geriatric assessment was used to calculate the MPI and to categorize participants in low-, moderate-, and high-risk classes. The results were reported as hazard ratios (HRs) and the accuracy was evaluated with the area under the curve (AUC), with 95% confidence intervals (CIs) and the C-index. We also reported the median survival time by standard age groups. Results: All 1453 participants (mean age 68.9 years, women = 55.8%) enrolled in the InCHIANTI study at baseline were included. Compared to low-risk group, participants in moderate (HR = 2.10; 95% CI: 1.73-2.55) and high-risk MPI group (HR = 4.94; 95% CI: 3.91-6.24) had significantly higher mortality risk. The C-index of the model containing age, sex, and MPI was 82.1, indicating a very good accuracy of this model in explaining mortality. Additionally, the time-dependent AUC indicated that the accuracy of the model incorporating MPI to age and sex was excellent (>85.0) during the whole follow-up period. Compared to participants in the low-risk MPI group across different age groups, those in moderate- and high-risk groups survived 2.9-7.0 years less and 4.3-8.9 years less, respectively. Conclusions: In community-dwelling individuals, higher MPI values are associated with higher risk of all-cause mortality with a dose-response effect. © 2020 The Author(s) 2020

Efficient Linear Bandits through Matrix Sketching

We prove that two popular linear contextual bandit algorithms, OFUL and Thompson Sampling, can be made efficient using Frequent Directions, a deterministic online sketching technique. More precisely, we show that a sketch of size m allows a O(md) update time for both algorithms, as opposed to \u2126(d 2 ) required by their non-sketched versions in general (where d is the dimension of context vectors). This computational speedup is accompanied by regret bounds of order (1 + \u3b5m) 3/2d 1a T for OFUL and of order (1 + \u3b5m)d 3/2 1a T for Thompson Sampling, where \u3b5m is bounded by the sum of the tail eigenvalues not covered by the sketch. In particular, when the selected contexts span a subspace of dimension at most m, our algorithms have a regret bound matching that of their slower, non-sketched counterparts. Experiments on real-world datasets corroborate our theoretical results

Optical response of a misaligned and suspended Fabry-Perot cavity

The response to a probe laser beam of a suspended, misaligned and detuned optical cavity is examined. A five degree of freedom model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product $\varpi \tau$ of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility.Comment: 14 pages (4 figures) submitted to Phys. Rev.

The Impact of the First and Second Wave of the COVID-19 Pandemic on Eating Symptoms and Dysfunctional Eating Behaviours in the General Population: A Systematic Review and Meta-Analysis

Background: The aim of this systematic review and meta-analysis was to examine the prevalence of feeding and eating disorder (FED) symptoms or dysfunctional eating behaviours (DEB) in the general population during the COVID-19 outbreak. Method: We searched eligible articles in biomedical databases from 1 January 2020 to 31 March 2022. Prevalence rates of FED or DEB changes between pre-pandemic and pandemic time and correlation with psychological distress were pooled with a meta-analysis using a random-effects model. Heterogeneity was tested using I-squared (I2) statistics. A total of 186 studies with 406,076 participants met the inclusion criteria. Results: The more prevalent FED or DEB during the COVID-19 outbreak were: body image concerns (52%, 95% CI 0.38, 0.66), binge eating (40%, 95% CI 0.25, 0.55), and overeating (40%, 95% CI = 0.32-0.48). Pooled data of longitudinal studies (k = 8) only showed a significant difference in the prevalence of weight gain from pre-pandemic to the pandemic time. Finally, increased levels of psychological distress (k = 35) positively correlated with some ED symptoms. Conclusion: This meta-analysis evidenced a negative impact of the pandemic on eating symptoms and DEB in the general population

Constraints From b→sγb \to s\gamma on the Left-Right Symmetric Model

Recent results from the CLEO Collaboration on both inclusive and exclusive radiative $B$ decays are used to constrain the parameter space of two versions of the Left-Right Symmetric Model. In the first scenario, when the left- and right-handed Cabibbo-Kobayashi-Maskawa mixing matrices are equal, $V_L=V_R$, the radiative $B$ decay data is shown to lead to strong bounds on the $W_L-W_R$ mixing angle that are quite insensitive to either the top quark or $W_R$ mass. The second scenario examined is that of Gronau and Wakaizumi wherein $b$-quark decays proceed only via right-handed currents and $V_L$ and $V_R$ are quite distinct. For this model, the combined constraints from Tevatron $W_R$ searches, the $B$ lifetime, and radiative $B$ decays lead to a very highly restricted allowed range for the $W_L-W_R$ mixing angle.Comment: 16 pages, 9 figures(not included), LaTex, SLAC-PUB-642

The b→sγγb\to s\gamma\gamma transition in softly broken supersymmetry

We study the effect of supersymmetric contributions to the effective quark transition $b\to s\gamma\gamma$, including leading order QCD effects. We apply the discussion to the decay $B_s\to\gamma\gamma$. Even though one-particle irreducible contributions could play a role, numerical cancelations make the amplitude for the two-photon emission strongly correlated to the $b\to s\gamma$ amplitude which is sharply constrained by experiment. A quite general statement follows: as long as non-standard physics effects appear only in the matching of the Wilson coefficients of the standard effective operator basis, the deviations from the standard model expectations of the decay rates induced by $b\to s\gamma\gamma$ are bound to follow closely the corresponding deviations on $b\to s\gamma$. Effects of new physics are therefore bound to be small.Comment: Latex2e, RevTex, 22 pages, 8 eps figures, comments and references adde

Using b→sγb \to s\gamma to Probe Top Quark Couplings

Possible anomalous couplings of the top-quark to on-shell photons and gluons are constrained by the recent results of the CLEO Collaboration on both inclusive and exclusive radiative $B$ decays. We find that the process \bsg\ can lead to reasonable bounds on both the anomalous electric and magnetic dipole moments of the top-quark, while essentially no limits are obtained on the corresponding chromoelectric and chromomagnetic moments, which enter the expression for the decay rate only through operator mixing.Comment: 10 pages plus 6 figures (available by request), LaTex, ANL-HEP-PR-93-3

The CP asymmetry for B--> K^* l^+ l^- decay in the general two Higgs doublet model

We study CP asymmetry for the exclusive decay B --> K^* l^+ l^- in the two Higgs doublet model with three level flavor changing neutral currents (model III). We analyse the dependency of this quantity to the new phase coming from the complex Yukawa couplings in the theory and we find that there exist a considerable CP violation for the relevant process. Further, we see that the sign of the Wilson coefficient C_7^{eff} can be determined by fixing dilepton mass. Therefore, the future measurements of CP asymmetry for B --> K^* l^+ l^- decay will give a powerful information about the sign of Wilson coefficient C_{7}^{eff} and the new physics beyond the SM.Comment: 22 pages, 8 figure

CP Violation in the Decay B \to X_d e^+ e^-

The decay $b\to d e^+e^-$ has an amplitude containing comparable contributions proportional to $V_{tb}V_{td}^{*}$, $V_{cb}V_{cd}^{*}$ and $V_{ub}V_{ud}^{*}$. These pieces involve different unitarity phases produced by $c\bar{c}$ and $u\bar{u}$ loops. The simultaneous presence of different CKM phases and different dynamical phases leads to a calculable asymmetry in the partial widths of $b\to d e^+e^-$ and $\bar{b}\to \bar{d} e^+e^-$. Using the effective Hamiltonian of the standard model, we calculate this asymmetry as a function of the $e^+e^-$ invariant mass. The effects of $\rho$, $\omega$ and $J/\psi$ resonances are taken into account in the vacuum polarization of the $u\bar{u}$ and $c\bar{c}$ currents. As a typical result, an asymmetry of $- 5(- 2$ is predicted in the nonresonant domain $1 GeV < m_{e^+e^-} < m_{J/\psi}$, assuming $\eta = 0.34$ and $\rho= 0.3 (-0.3)$. The branching ratio in this domain is $1.2\times 10^{-7} (3.3\times 10^{-7})$. Results are also obtained in the region of the $J/\psi$ resonance, where an asymmetry of $3\times 10^{-3}$ is expected, subject to certain theoretical uncertainties in the $b\to d J/\psi$ amplitude.Comment: 20 pages, LaTeX, 3 eps figures, uses cite.sty, epsf.sty, and amssym.sty. Version to appear in Phys. Rev. D, with some minor addition