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The dueling bandits problem has received a lot of attention in recent years due to its applications in recommendation systems and information retrieval. However, due to the prevalence of malicious users in these systems, it is becoming increasingly important to design dueling bandit algorithms that are robust to corruptions introduced by these malicious users. In this paper we study dueling bandits in the presence of an adversary that can corrupt some of the feedback received by the learner. We propose an algorithm for this problem that is agnostic to the amount of corruption introduced by the adversary: its regret degrades gracefully with the amount of corruption, and in case of no corruption, it essentially matches the optimal regret bounds achievable in the purely stochastic dueling bandits setting. 

The effect of nozzle surface features on the overall atomization behavior of a liquid jet is analyzed in the present computational work by adopting three representative geometries, namely a single X-ray tomography scan of the Engine Combustion Network’s Spray A nozzle (Unprocessed), a spline reconstruction of multiple scans (Educated), and a purely external flow configuration. The latter configuration is often used in fundamental jet atomization studies. Numerically, the two-phase flow is solved based on algebraic volume-of-fluid methodology utilizing the OpenFoam solver, interFoam. Quantitative characterization of the surface features concerning the first two geometries reveals that while both of them have similar levels of cylindrical asymmetries, the nozzle configuration pertaining to the Unprocessed geometry has much larger surface features along the streamwise direction than the Educated geometry. This produces for the Unprocessed configuration a much larger degree of non-axial velocity components in the flow exiting the orifice and also a more pronounced disturbance of the liquid surface in the first few diameters downstream of the nozzle orifice. Furthermore, this heightened level of surface destabilization generates a much shorter intact liquid core length, that is, it produces faster primary atomization. The surprising aspect of this finding is that the differences between the Unprocessed and Educated geometries are of [Formula: see text](1) μm, and they are able to produce [Formula: see text](1) mm effects in the intact liquid core length. In spite of more pronounced atomization for the Unprocessed geometry, the magnitude of the turbulent liquid kinetic energy is roughly the same as the Educated geometry. This highlights the important role of mean field quantities, in particular, non-axial velocity components, in precipitating primary atomization. At the other end of the spectrum, the external-only configuration has the mildest level of surface disturbances in the near field resulting in the longest intact liquid core length. 

Rank aggregation from pairwise preferences has widespread applications in recommendation systems and information retrieval. Given the enormous economic and societal impact of these applications, and the consequent incentives for malicious players to manipulate ranking outcomes in their favor, an important challenge is to make rank aggregation algorithms robust to adversarial manipulations in data. In this paper, we initiate the study of robustness in rank aggregation under the popular Bradley-Terry-Luce (BTL) model for pairwise comparisons. We consider a setting where pairwise comparisons are initially generated according to a BTL model, but a fraction of these comparisons are corrupted by an adversary prior to being reported to us. We consider a strong contamination model, where an adversary having complete knowledge of the initial truthful data and the underlying true BTL parameters, can subsequently corrupt the truthful data by inserting, deleting, or changing data points. The goal is to estimate the true score/weight of each item under the BTL model, even in the presence of these corruptions. We characterize the extent of adversarial corruption under which the true BTL parameters are uniquely identifiable. We also provide a novel pruning algorithm that provably cleans the data of adversarial corruption under reasonable conditions on data generation and corruption. We corroborate our theory with experiments on both synthetic as well as real data showing that previous algorithms are vulnerable to even small amounts of corruption, whereas our algorithm can clean a reasonably high amount of corruption.