Learning optimization models in the presence of unknown relations

In a sequential auction with multiple bidding agents, it is highly challenging to determine the ordering of the items to sell in order to maximize the revenue due to the fact that the autonomy and private information of the agents heavily influence the outcome of the auction. The main contribution of this paper is two-fold. First, we demonstrate how to apply machine learning techniques to solve the optimal ordering problem in sequential auctions. We learn regression models from historical auctions, which are subsequently used to predict the expected value of orderings for new auctions. Given the learned models, we propose two types of optimization methods: a black-box best-first search approach, and a novel white-box approach that maps learned models to integer linear programs (ILP) which can then be solved by any ILP-solver. Although the studied auction design problem is hard, our proposed optimization methods obtain good orderings with high revenues. Our second main contribution is the insight that the internal structure of regression models can be efficiently evaluated inside an ILP solver for optimization purposes. To this end, we provide efficient encodings of regression trees and linear regression models as ILP constraints. This new way of using learned models for optimization is promising. As the experimental results show, it significantly outperforms the black-box best-first search in nearly all settings.Comment: 37 pages. Working pape

Fair task allocation in transportation

Task allocation problems have traditionally focused on cost optimization. However, more and more attention is being given to cases in which cost should not always be the sole or major consideration. In this paper we study a fair task allocation problem in transportation where an optimal allocation not only has low cost but more importantly, it distributes tasks as even as possible among heterogeneous participants who have different capacities and costs to execute tasks. To tackle this fair minimum cost allocation problem we analyze and solve it in two parts using two novel polynomial-time algorithms. We show that despite the new fairness criterion, the proposed algorithms can solve the fair minimum cost allocation problem optimally in polynomial time. In addition, we conduct an extensive set of experiments to investigate the trade-off between cost minimization and fairness. Our experimental results demonstrate the benefit of factoring fairness into task allocation. Among the majority of test instances, fairness comes with a very small price in terms of cost

Interpretations and Implications of the Top Quark Rapidity Asymmetries AFBtA_{FB}^t and AFBℓA_{FB}^{\ell}

Forward-backward asymmetries $A_{FB}^t$ and $A_{FB}^\ell$ are observed in the top quark $t$ rapidity distribution and in the rapidity distribution of charged leptons $\ell$ from top quark decay at the Tevatron proton-antiproton collider, and a charge asymmetry $A_C$ is seen in proton-proton collisions at the Large Hadron Collider (LHC). In this paper, we update our previous studies of the Tevatron asymmetries using the most recent data. We provide expectations for $A_C$ at the LHC based first on model independent extrapolations from the Tevatron, and second based on new physics models that can explain the Tevatron asymmetries. We examine the relationship of the two asymmetries $A_{FB}^t$ and $A_{FB}^\ell$. We show their connection through the $(V-A)$ spin correlation between the charged lepton and the top quark with different polarization states. We show that the ratio of the two asymmetries provides independent insight into new physics models that are invoked to fit the top quark asymmetry. We emphasize the value of the measurement of both asymmetries, and we conclude that a model which produces more right-handed than left-handed top quarks is favored by the present Tevatron data.Comment: Some figures changed. A typo in appendix fixed. Published in Physical Review

Top Quark Polarization As A Probe of Models with Extra Gauge Bosons

New heavy gauge bosons exist in many models of new physics beyond the standard model of particle physics. Discovery of these W^\prime and Z^\prime resonances and the establishment of their spins, couplings, and other quantum numbers would shed light on the gauge structure of the new physics. The measurement of the polarization of the SM fermions from the gauge boson decays would decipher the handedness of the coupling of the new states, an important relic of the primordial new physics symmetry. Since the top quark decays promptly, its decay preserves spin information. We show how decays of new gauge bosons into third generation fermions (W^\prime \to tb, Z^\prime\to t\bar{t}) can be used to determine the handedness of the couplings of the new states and to discriminate among various new physics models

Top Quark Forward-Backward Asymmetry and Same-Sign Top Quark Pairs

The top quark forward-backward asymmetry measured at the Tevatron collider shows a large deviation from standard model expectations. Among possible interpretations, a non-universal $Z^\prime$ model is of particular interest as it naturally predicts a top quark in the forward region of large rapidity. To reproduce the size of the asymmetry, the couplings of the $Z^\prime$ to standard model quarks must be large, inevitably leading to copious production of same-sign top quark pairs at the energies of the Large Hadron Collider (LHC). We explore the discovery potential for $tt$ and $ttj$ production in early LHC experiments at 7-8 TeV and conclude that if {\it no} $tt$ signal is observed with 1 fb$^{-1}$ of integrated luminosity, then a non-universal $Z^\prime$ alone cannot explain the Tevatron forward-backward asymmetry.Comment: Tevatron limit from same-sign tt search adde

The Top Quark Production Asymmetries AFBtA_{FB}^t and AFBℓA_{FB}^{\ell}

A large forward-backward asymmetry is seen in both the top quark rapidity distribution $A_{FB}^t$ and in the rapidity distribution of charged leptons $A_{FB}^\ell$ from top quarks produced at the Tevatron. We study the kinematic and dynamic aspects of the relationship of the two observables arising from the spin correlation between the charged lepton and the top quark with different polarization states. We emphasize the value of both measurements, and we conclude that a new physics model which produces more right-handed than left-handed top quarks is favored by the present data.Comment: accepted for publication in Physical Review Letter