Restricted Adaptivity in Stochastic Scheduling

We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee ?((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of ?-delay and ?-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an ?(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any ?-delay and ?-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy

On the Complexity of Computing Sparse Equilibria and Lower Bounds for No-Regret Learning in Games

Characterizing the performance of no-regret dynamics in multi-player games is a foundational problem at the interface of online learning and game theory. Recent results have revealed that when all players adopt specific learning algorithms, it is possible to improve exponentially over what is predicted by the overly pessimistic no-regret framework in the traditional adversarial regime, thereby leading to faster convergence to the set of coarse correlated equilibria (CCE). Yet, despite considerable recent progress, the fundamental complexity barriers for learning in normal- and extensive-form games are poorly understood. In this paper, we make a step towards closing this gap by first showing that -- barring major complexity breakthroughs -- any polynomial-time learning algorithms in extensive-form games need at least $2^{\log^{1/2 - o(1)} |\mathcal{T}|}$ iterations for the average regret to reach below even an absolute constant, where $|\mathcal{T}|$ is the number of nodes in the game. This establishes a superpolynomial separation between no-regret learning in normal- and extensive-form games, as in the former class a logarithmic number of iterations suffices to achieve constant average regret. Furthermore, our results imply that algorithms such as multiplicative weights update, as well as its \emph{optimistic} counterpart, require at least $2^{(\log \log m)^{1/2 - o(1)}}$ iterations to attain an $O(1)$-CCE in $m$-action normal-form games. These are the first non-trivial -- and dimension-dependent -- lower bounds in that setting for the most well-studied algorithms in the literature. From a technical standpoint, we follow a beautiful connection recently made by Foster, Golowich, and Kakade (ICML '23) between sparse CCE and Nash equilibria in the context of Markov games. Consequently, our lower bounds rule out polynomial-time algorithms well beyond the traditional online learning framework.Comment: To appear at ITCS 202

Approximation results for makespan minimization with budgeted uncertainty

International audienceWe study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to [3], once the schedule is defined an adversary can pick a scenario where deviation is added to some of the jobs' processing times. Given only the maximal cardinality of these jobs, and the magnitude of potential deviation for each job, the goal is to optimize the worst-case scenario. We consider both the cases of identical and unrelated machines. Our main result is an EPTAS for the case of identical machines. We also provide a 3-approximation algorithm and an inapproximability ratio of 2 − epsilon for the case of unrelated machines

Novel approaches to anonymity and privacy in decentralized, open settings

The Internet has undergone dramatic changes in the last two decades, evolving from a mere communication network to a global multimedia platform in which billions of users actively exchange information. While this transformation has brought tremendous benefits to society, it has also created new threats to online privacy that existing technology is failing to keep pace with. In this dissertation, we present the results of two lines of research that developed two novel approaches to anonymity and privacy in decentralized, open settings. First, we examine the issue of attribute and identity disclosure in open settings and develop the novel notion of (k,d)-anonymity for open settings that we extensively study and validate experimentally. Furthermore, we investigate the relationship between anonymity and linkability using the notion of (k,d)-anonymity and show that, in contrast to the traditional closed setting, anonymity within one online community does necessarily imply unlinkability across different online communities in the decentralized, open setting. Secondly, we consider the transitive diffusion of information that is shared in social networks and spread through pairwise interactions of user connected in this social network. We develop the novel approach of exposure minimization to control the diffusion of information within an open network, allowing the owner to minimize its exposure by suitably choosing who they share their information with. We implement our algorithms and investigate the practical limitations of user side exposure minimization in large social networks. At their core, both of these approaches present a departure from the provable privacy guarantees that we can achieve in closed settings and a step towards sound assessments of privacy risks in decentralized, open settings.Das Internet hat in den letzten zwei Jahrzehnten eine drastische Transformation erlebt und entwickelte sich dabei von einem einfachen Kommunikationsnetzwerk zu einer globalen Multimedia Plattform auf der Milliarden von Nutzern aktiv Informationen austauschen. Diese Transformation hat zwar einen gewaltigen Nutzen und vielfältige Vorteile für die Gesellschaft mit sich gebracht, hat aber gleichzeitig auch neue Herausforderungen und Gefahren für online Privacy mit sich gebracht mit der die aktuelle Technologie nicht mithalten kann. In dieser Dissertation präsentieren wir zwei neue Ansätze für Anonymität und Privacy in dezentralisierten und offenen Systemen. Mit unserem ersten Ansatz untersuchen wir das Problem der Attribut- und Identitätspreisgabe in offenen Netzwerken und entwickeln hierzu den Begriff der (k, d)-Anonymität für offene Systeme welchen wir extensiv analysieren und anschließend experimentell validieren. Zusätzlich untersuchen wir die Beziehung zwischen Anonymität und Unlinkability in offenen Systemen mithilfe des Begriff der (k, d)-Anonymität und zeigen, dass, im Gegensatz zu traditionell betrachteten, abgeschlossenen Systeme, Anonymität innerhalb einer Online Community nicht zwingend die Unlinkability zwischen verschiedenen Online Communitys impliziert. Mit unserem zweiten Ansatz untersuchen wir die transitive Diffusion von Information die in Sozialen Netzwerken geteilt wird und sich dann durch die paarweisen Interaktionen von Nutzern durch eben dieses Netzwerk ausbreitet. Wir entwickeln eine neue Methode zur Kontrolle der Ausbreitung dieser Information durch die Minimierung ihrer Exposure, was dem Besitzer dieser Information erlaubt zu kontrollieren wie weit sich deren Information ausbreitet indem diese initial mit einer sorgfältig gewählten Menge von Nutzern geteilt wird. Wir implementieren die hierzu entwickelten Algorithmen und untersuchen die praktischen Grenzen der Exposure Minimierung, wenn sie von Nutzerseite für große Netzwerke ausgeführt werden soll. Beide hier vorgestellten Ansätze verbindet eine Neuausrichtung der Aussagen die diese bezüglich Privacy treffen: wir bewegen uns weg von beweisbaren Privacy Garantien für abgeschlossene Systeme, und machen einen Schritt zu robusten Privacy Risikoeinschätzungen für dezentralisierte, offene Systeme in denen solche beweisbaren Garantien nicht möglich sind

Oracle-Efficient Differentially Private Learning with Public Data

Due to statistical lower bounds on the learnability of many function classes under privacy constraints, there has been recent interest in leveraging public data to improve the performance of private learning algorithms. In this model, algorithms must always guarantee differential privacy with respect to the private samples while also ensuring learning guarantees when the private data distribution is sufficiently close to that of the public data. Previous work has demonstrated that when sufficient public, unlabelled data is available, private learning can be made statistically tractable, but the resulting algorithms have all been computationally inefficient. In this work, we present the first computationally efficient, algorithms to provably leverage public data to learn privately whenever a function class is learnable non-privately, where our notion of computational efficiency is with respect to the number of calls to an optimization oracle for the function class. In addition to this general result, we provide specialized algorithms with improved sample complexities in the special cases when the function class is convex or when the task is binary classification

Information-Distilling Quantizers

Let $X$ and $Y$ be dependent random variables. This paper considers the problem of designing a scalar quantizer for $Y$ to maximize the mutual information between the quantizer's output and $X$, and develops fundamental properties and bounds for this form of quantization, which is connected to the log-loss distortion criterion. The main focus is the regime of low $I(X;Y)$, where it is shown that, if $X$ is binary, a constant fraction of the mutual information can always be preserved using $\mathcal{O}(\log(1/I(X;Y)))$ quantization levels, and there exist distributions for which this many quantization levels are necessary. Furthermore, for larger finite alphabets $2 < |\mathcal{X}| < \infty$, it is established that an $\eta$-fraction of the mutual information can be preserved using roughly $(\log(| \mathcal{X} | /I(X;Y)))^{\eta\cdot(|\mathcal{X}| - 1)}$ quantization levels