539 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Game-theoretic statistics and safe anytime-valid inference

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    Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring and analysis of accumulating data and optional stopping or continuation for any reason. These measures crucially rely on test martingales, which are nonnegative martingales starting at one. Since a test martingale is the wealth process of a player in a betting game, SAVI centrally employs game-theoretic intuition, language and mathematics. We summarize the SAVI goals and philosophy, and report recent advances in testing composite hypotheses and estimating functionals in nonparametric settings.Comment: 25 pages. Under review. ArXiv does not compile/space some references properl

    Towards compact bandwidth and efficient privacy-preserving computation

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    In traditional cryptographic applications, cryptographic mechanisms are employed to ensure the security and integrity of communication or storage. In these scenarios, the primary threat is usually an external adversary trying to intercept or tamper with the communication between two parties. On the other hand, in the context of privacy-preserving computation or secure computation, the cryptographic techniques are developed with a different goal in mind: to protect the privacy of the participants involved in a computation from each other. Specifically, privacy-preserving computation allows multiple parties to jointly compute a function without revealing their inputs and it has numerous applications in various fields, including finance, healthcare, and data analysis. It allows for collaboration and data sharing without compromising the privacy of sensitive data, which is becoming increasingly important in today's digital age. While privacy-preserving computation has gained significant attention in recent times due to its strong security and numerous potential applications, its efficiency remains its Achilles' heel. Privacy-preserving protocols require significantly higher computational overhead and bandwidth when compared to baseline (i.e., insecure) protocols. Therefore, finding ways to minimize the overhead, whether it be in terms of computation or communication, asymptotically or concretely, while maintaining security in a reasonable manner remains an exciting problem to work on. This thesis is centred around enhancing efficiency and reducing the costs of communication and computation for commonly used privacy-preserving primitives, including private set intersection, oblivious transfer, and stealth signatures. Our primary focus is on optimizing the performance of these primitives.Im Gegensatz zu traditionellen kryptografischen Aufgaben, bei denen Kryptografie verwendet wird, um die Sicherheit und Integrität von Kommunikation oder Speicherung zu gewährleisten und der Gegner typischerweise ein Außenstehender ist, der versucht, die Kommunikation zwischen Sender und Empfänger abzuhören, ist die Kryptografie, die in der datenschutzbewahrenden Berechnung (oder sicheren Berechnung) verwendet wird, darauf ausgelegt, die Privatsphäre der Teilnehmer voreinander zu schützen. Insbesondere ermöglicht die datenschutzbewahrende Berechnung es mehreren Parteien, gemeinsam eine Funktion zu berechnen, ohne ihre Eingaben zu offenbaren. Sie findet zahlreiche Anwendungen in verschiedenen Bereichen, einschließlich Finanzen, Gesundheitswesen und Datenanalyse. Sie ermöglicht eine Zusammenarbeit und Datenaustausch, ohne die Privatsphäre sensibler Daten zu kompromittieren, was in der heutigen digitalen Ära immer wichtiger wird. Obwohl datenschutzbewahrende Berechnung aufgrund ihrer starken Sicherheit und zahlreichen potenziellen Anwendungen in jüngster Zeit erhebliche Aufmerksamkeit erregt hat, bleibt ihre Effizienz ihre Achillesferse. Datenschutzbewahrende Protokolle erfordern deutlich höhere Rechenkosten und Kommunikationsbandbreite im Vergleich zu Baseline-Protokollen (d.h. unsicheren Protokollen). Daher bleibt es eine spannende Aufgabe, Möglichkeiten zu finden, um den Overhead zu minimieren (sei es in Bezug auf Rechen- oder Kommunikationsleistung, asymptotisch oder konkret), während die Sicherheit auf eine angemessene Weise gewährleistet bleibt. Diese Arbeit konzentriert sich auf die Verbesserung der Effizienz und Reduzierung der Kosten für Kommunikation und Berechnung für gängige datenschutzbewahrende Primitiven, einschließlich private Schnittmenge, vergesslicher Transfer und Stealth-Signaturen. Unser Hauptaugenmerk liegt auf der Optimierung der Leistung dieser Primitiven

    Perfect Sampling for Hard Spheres from Strong Spatial Mixing

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    We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials

    Sample Complexity Analysis for Adaptive Optimization Algorithms with Stochastic Oracles

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    Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic oracles. Unlike the majority of stochastic methods, these methods do not use a pre-specified sequence of step size parameters, but adapt the step size parameter according to the estimated progress of the algorithm and use it to dictate the accuracy required from the stochastic approximations. The requirements on stochastic approximations are, thus, also adaptive and the oracle costs can vary from iteration to iteration. The step size parameters in these methods can increase and decrease based on the perceived progress, but unlike the deterministic case they are not bounded away from zero due to possible oracle failures, and bounds on the step size parameter have not been previously derived. This creates obstacles in the total complexity analysis of such methods, because the oracle costs are typically decreasing in the step size parameter, and could be arbitrarily large as the step size parameter goes to 0. Thus, until now only the total iteration complexity of these methods has been analyzed. In this paper, we derive a lower bound on the step size parameter that holds with high probability for a large class of adaptive stochastic methods. We then use this lower bound to derive a framework for analyzing the expected and high probability total oracle complexity of any method in this class. Finally, we apply this framework to analyze the total sample complexity of two particular algorithms, STORM and SASS, in the expected risk minimization problem

    On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks

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    Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the globalglobal effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima. We show that QTW achieves quantum speedup over classical stochastic gradient descents (SGD) when the barriers between different local minima are high but thin and the minima are flat. Based on this observation, we construct a specific double-well landscape, where classical algorithms cannot efficiently hit one target well knowing the other well but QTW can when given proper initial states near the known well. Finally, we corroborate our findings with numerical experiments

    Quantum Computing for Airline Planning and Operations

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    Classical algorithms and mathematical optimization techniques have beenused extensively by airlines to optimize their profit and ensure that regulationsare followed. In this thesis, we explore which role quantum algorithmscan have for airlines. Specifically, we have considered the two quantum optimizationalgorithms; the Quantum Approximate Optimization Algorithm(QAOA) and Quantum Annealing (QA). We present a heuristic that integratesthese quantum algorithms into the existing classical algorithm, whichis currently employed to solve airline planning problems in a state-of-the-artcommercial solver. We perform numerical simulations of QAOA circuits andfind that linear and quadratic algorithm depth in the input size can be requiredto obtain a one-shot success probability of 0.5. Unfortunately, we areunable to find performance guarantees. Finally, we perform experiments withD-wave’s newly released QA machine and find that it outperforms 2000Q formost instances

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Sample efficient graph classification using binary Gaussian boson sampling

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    We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS) a near term model of quantum computing. However, unlike the currently proposed algorithms for this problem, our GBS setup only requires binary (light/no light) detectors, as opposed to photon number resolving detectors. These detectors are technologically simpler and can operate at room temperature, making our algorithm less complex and less costly to implement on the physical hardware. We also investigate the connection between graph theory and the matrix function called the Torontonian which characterizes the probabilities of binary GBS detection events
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