On the Prior Sensitivity of Thompson Sampling

The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(\sqrt{T/p})$ and $O(\sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as \emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge.Comment: Appears in the 27th International Conference on Algorithmic Learning Theory (ALT), 201

Efficient approximate thompson sampling for search query recommendation

Query suggestions have been a valuable feature for e-commerce sites in helping shoppers refine their search intent. In this paper, we develop an algorithm that helps e-commerce sites like eBay mingle the output of different recommendation al-gorithms. Our algorithm is based on “Thompson Sampling” — a technique designed for solving multi-arm bandit prob-lems where the best results are not known in advance but instead are tried out to gather feedback. Our approach is to treat query suggestions as a competition among data re-sources: we have many query suggestion candidates compet-ing for limited space on the search results page. An “arm” is played when a query suggestion candidate is chosen for display, and our goal is to maximize the expected reward (user clicks on a suggestion). Our experiments have shown promising results in using the click-based user feedback to drive success by enhancing the quality of query suggestions

Structure and Melting of Two-Species Charged Clusters in a Parabolic Trap

We consider a system of charged particles interacting with an unscreened Coulomb repulsion in a two-dimensional parabolic confining trap. The static charge on a portion of the particles is twice as large as the charge on the remaining particles. The particles separate into a shell structure with those of greater charge situated farther from the center of the trap. As we vary the ratio of the number of particles of the two species, we find that for certain configurations, the symmetry of the arrangement of the inner cluster of singly-charged particles matches the symmetry of the outer ring of doubly-charged particles. These matching configurations have a higher melting temperature and a higher thermal threshold for intershell rotation between the species than the nonmatching configurations.Comment: 4 pages, 6 postscript figure

Yield conditions for deformation of amorphous polymer glasses

Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset of shear is consistent with the pressure-modified von Mises criterion, and the pressure coefficient is nearly independent of many parameters. Under triaxial tensile loading, the mode of failure changes to cavitation.Comment: 9 pages, 8 figures, revte

»Filozofija i kršćanstvo« »Philosophia et christianita«

This work was undertaken during T.L. Stephens’s PhD studentship, supported by the Central England Natural Environmental Research Council (NERC) Training Alliance (CENTA) [award reference: 1503848]. The authors would like to thank Nicolas Le Corvec and an anonymous reviewer for their helpful comments during the reviewing process. Additionally we would like to thank Craig Magee, Atsushi Yamaji, and an anonymous reviewer for their constructive reviews on an earlier version of the manuscript.Peer reviewedPublisher PD

Hard-core Yukawa model for two-dimensional charge stabilized colloids

The hyper-netted chain (HNC) and Percus-Yevick (PY) approximations are used to study the phase diagram of a simple hard-core Yukawa model of charge-stabilized colloidal particles in a two-dimensional system. We calculate the static structure factor and the pair distribution function over a wide range of parameters. Using the statics correlation functions we present an estimate for the liquid-solid phase diagram for the wide range of the parameters.Comment: 7 pages, 9figure

Brownian motion exhibiting absolute negative mobility

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).Comment: 4 pages, 3 figures, to be published in PR

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

Transition Between Ground State and Metastable States in Classical 2D Atoms

Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the Newton optimization technique. This system is the classical analog of the well-known quantum dot problem. The energies and configurations of the ground and all metastable states are obtained. In order to investigate the barriers and the transitions between the ground and all metastable states we first locate the saddle points between them, then by walking downhill from the saddle point to the different minima, we find the path in configurational space from the ground state to the metastable states, from which the geometric properties of the energy landscape are obtained. The sensitivity of the ground-state configuration on the functional form of the inter-particle interaction and on the confinement potential is also investigated

Derivation, validation, and clinical relevance of a pediatric sepsis phenotype with persistent hypoxemia, encephalopathy, and shock

OBJECTIVES: Untangling the heterogeneity of sepsis in children and identifying clinically relevant phenotypes could lead to the development of targeted therapies. Our aim was to analyze the organ dysfunction trajectories of children with sepsis-associated multiple organ dysfunction syndrome (MODS) to identify reproducible and clinically relevant sepsis phenotypes and determine if they are associated with heterogeneity of treatment effect (HTE) to common therapies. DESIGN: Multicenter observational cohort study. SETTING: Thirteen PICUs in the United States. PATIENTS: Patients admitted with suspected infections to the PICU between 2012 and 2018. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We used subgraph-augmented nonnegative matrix factorization to identify candidate trajectory-based phenotypes based on the type, severity, and progression of organ dysfunction in the first 72 hours. We analyzed the candidate phenotypes to determine reproducibility as well as prognostic, therapeutic, and biological relevance. Overall, 38,732 children had suspected infection, of which 15,246 (39.4%) had sepsis-associated MODS with an in-hospital mortality of 10.1%. We identified an organ dysfunction trajectory-based phenotype (which we termed persistent hypoxemia, encephalopathy, and shock) that was highly reproducible, had features of systemic inflammation and coagulopathy, and was independently associated with higher mortality. In a propensity score-matched analysis, patients with persistent hypoxemia, encephalopathy, and shock phenotype appeared to have HTE and benefit from adjuvant therapy with hydrocortisone and albumin. When compared with other high-risk clinical syndromes, the persistent hypoxemia, encephalopathy, and shock phenotype only overlapped with 50%-60% of patients with septic shock, moderate-to-severe pediatric acute respiratory distress syndrome, or those in the top tier of organ dysfunction burden, suggesting that it represents a nonsynonymous clinical phenotype of sepsis-associated MODS. CONCLUSIONS: We derived and validated the persistent hypoxemia, encephalopathy, and shock phenotype, which is highly reproducible, clinically relevant, and associated with HTE to common adjuvant therapies in children with sepsis