arXiv subjects

Asaf Cohen

Publications and source records attributed to Asaf Cohen.

At least 55 records · Page 3Linked to original sources

arXiv2021

Optimal ergodic harvesting under ambiguity

We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, the problem is constructed as a stochastic game with two players: the decision-maker (DM) chooses the `best' harvesting policy and an adverse player chooses the `worst' probability measure. The main result is establishing an optimal strategy (also referred to as a control) of the DM and showing that it is a threshold policy. The optimal threshold and the optimal payoff are obtained by solving a free-boundary problem emerging from the Hamilton--Jacobi--Bellman (HJB) equation. As part of the proof, we fix a gap that appeared in the HJB analysis of [Alvarez and Hening, {\em Stochastic Process. Appl.}, 2019], a paper that analyzed the risk-neutral version of the ergodic harvesting problem. Finally, we study the dependence of the optimal threshold and the optimal payoff on the ambiguity parameter and show that if the ambiguity goes to 0, the problem converges, to the risk-neutral problem.

math.OC↗

arXiv2021

Secure Multi-Source Multicast

The principal mission of Multi-Source Multicast (MSM) is to disseminate all messages from all sources in a network to all destinations. MSM is utilized in numerous applications. In many of them, securing the messages disseminated is critical. A common secure model is to consider a network where there is an eavesdropper which is able to observe a subset of the network links, and seek a code which keeps the eavesdropper ignorant regarding all the messages. While this is solved when all messages are located at a single source, Secure MSM (SMSM) is an open problem, and the rates required are hard to characterize in general. In this paper, we consider Individual Security, which promises that the eavesdropper has zero mutual information with each message individually. We completely characterize the rate region for SMSM under individual security, and show that such a security level is achievable at the full capacity of the network, that is, the cut-set bound is the matching converse, similar to non-secure MSM. Moreover, we show that the field size is similar to non-secure MSM and does not have to be larger due to the security constraint.

cs.IT↗

arXiv2021

Asymptotic optimality of the generalized $cμ$ rule under model uncertainty

We consider a critically-loaded multiclass queueing control problem with model uncertainty. The model consists of $I$ types of customers and a single server. At any time instant, a decision-maker (DM) allocates the server's effort to the customers. The DM's goal is to minimize a convex holding cost that accounts for the ambiguity with respect to the model, i.e., the arrival and service rates. For this, we consider an adversary player whose role is to choose the worst-case scenario. Specifically, we assume that the DM has a reference probability model in mind and that the cost function is formulated by the supremum over equivalent admissible probability measures to the reference measure with two components, the first is the expected holding cost, and the second one is a penalty for the adversary player for deviating from the reference model. The penalty term is formulated by a general divergence measure. We show that although that under the equivalent admissible measures the critically-load condition might be violated, the generalized $cμ$ rule is asymptotically optimal for this problem.

math.PR↗

arXiv2021

Finite state Mean Field Games with Wright-Fisher common noise

We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on the simplex whose characteristics solve the stochastic forward-backward system associated with the mean field game; see Cardaliaguet et al. (2019). We show that this equation, which is a non-linear version of the Kimura type equation studied in Epstein and Mazzeo (2013), has a unique smooth solution whenever the normal component of the drift at the boundary is strong enough. Among others, this requires a priori estimates of Hölder type for the corresponding Kimura operator when the drift therein is merely continuous.

math.PR↗

arXiv2020

On singular control problems, the time-stretching method, and the weak-M1 topology

We consider a general class of singular control problems with state constraints. Budhiraja and Ross (2006) established the existence of optimal controls for a relaxed version of this class of problems by using the so-called `time-stretching' method and the J1-topology. We show that the weak-M1 topology is better suited for establishing existence, since it allows to bypass the time-transformations, without any additional effort. Furthermore, we reveal how the time-scaling feature in the definition of the weak-M1 distance embeds the time-stretching method's scheme. This case study suggests that one can benefit from working with the weak-M1 topology in other singular control frameworks, such as queueing control problems under heavy traffic.

math.OC↗

arXiv2020

Optimal Dividend Problem: Asymptotic Analysis

We re-visit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those in Bäuerle (2004), but we obtain sharper results because we use a different technique for obtaining them. Specifically, Bäuerle (2004) uses probabilistic techniques and relies on convergence in distribution of the underlying processes. By contrast, we use comparison results from the theory of differential equations, and these methods allow us to determine the rate of convergence of the value functions in question.

math.OC↗

arXiv2020

Centralized vs Decentralized Targeted Brute-Force Attacks: Guessing with Side-Information

According to recent empirical studies, a majority of users have the same, or very similar, passwords across multiple password-secured online services. This practice can have disastrous consequences, as one password being compromised puts all the other accounts at much higher risk. Generally, an adversary may use any side-information he/she possesses about the user, be it demographic information, password reuse on a previously compromised account, or any other relevant information to devise a better brute-force strategy (so called targeted attack). In this work, we consider a distributed brute-force attack scenario in which $m$ adversaries, each observing some side information, attempt breaching a password secured system. We compare two strategies: an uncoordinated attack in which the adversaries query the system based on their own side-information until they find the correct password, and a fully coordinated attack in which the adversaries pool their side-information and query the system together. For passwords $\mathbf{X}$ of length $n$, generated independently and identically from a distribution $P_X$, we establish an asymptotic closed-form expression for the uncoordinated and coordinated strategies when the side-information $\mathbf{Y}_{(m)}$ are generated independently from passing $\mathbf{X}$ through a memoryless channel $P_{Y|X}$, as the length of the password $n$ goes to infinity. We illustrate our results for binary symmetric channels and binary erasure channels, two families of side-information channels which model password reuse. We demonstrate that two coordinated agents perform asymptotically better than any finite number of uncoordinated agents for these channels, meaning that sharing side-information is very valuable in distributed attacks.

cs.IT↗

arXiv2020

Secure Adaptive Group Testing

\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can influence the makeup of future tests. Using an information theoretic point of view, Aldridge $2012$ showed that in the regime of a few defectives, adaptivity does not help much, as the number of tests required is essentially the same as for non-adaptive GT. \emph{Secure GT} considers a scenario where there is an eavesdropper who may observe a fraction $δ$ of the tests results, yet should not be able to infer the status of the items. In the non-adaptive scenario, the number of tests required is $1/(1-δ)$ times the number of tests without the secrecy constraint. In this paper, we consider \emph{Secure Adaptive GT}. Specifically, when during the makeup of the pools one has access to a private feedback link from the lab, of rate $R_f$. We prove that the number of tests required for both correct reconstruction at the legitimate lab, with high probability, and negligible mutual information at the eavesdropper is $1/min\{1,1-δ+R_f\}$ times the number of tests required with no secrecy constraint. Thus, unlike non-secure GT, where an adaptive algorithm has only a mild impact, under a security constraint it can significantly boost performance. A key insight is that not only the adaptive link should disregard the actual test results and simply send keys, these keys should be enhanced through a "secret sharing" scheme before usage. We drive sufficiency and necessity bounds that completely characterizes the Secure Adaptive GT capacity.

cs.IT↗

arXiv2020

Secure Group Testing

The principal goal of Group Testing (GT) is to identify a small subset of "defective" items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one defective item, and is negative otherwise. GT algorithms are utilized in numerous applications, and in many of them maintaining the privacy of the tested items, namely, keeping secret whether they are defective or not, is critical. In this paper, we consider a scenario where there is an eavesdropper (Eve) who is able to observe a subset of the GT outcomes (pools). We propose a new non-adaptive Secure Group Testing (SGT) scheme based on information-theoretic principles. The new proposed test design keeps the eavesdropper ignorant regarding the items' status. Specifically, when the fraction of tests observed by Eve is $0 \leq δ<1$, we prove that with the naive Maximum Likelihood (ML) decoding algorithm the number of tests required for both correct reconstruction at the legitimate user (with high probability) and negligible information leakage to Eve is $\frac{1}{1-δ}$ times the number of tests required with no secrecy constraint for the fixed $K$ regime. By a matching converse, we completely characterize the Secure GT capacity. Moreover, we consider the Definitely Non-Defective (DND) computationally efficient decoding algorithm, proposed in the literature for non-secure GT. We prove that with the new secure test design, for $δ< 1/2$, the number of tests required, without any constraint on $K$, is at most $\frac{1}{1/2-δ}$ times the number of tests required with no secrecy constraint.

cs.IT↗

arXiv2020

Multi-Antenna Jamming in Covert Communication

Covert communication conceals transmission of messages from Alice to Bob out of a watchful adversary, Willie, who tries to determine if a transmission took place or not. While covert communication in a basic, vanilla setting where all variables are known to Willie, results in the well-known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, a strictly positive transmission rate is possible. In this work, we analyze the case where the jammer is equipped with multiple antennas. Specifically, we analyze the effect of multiple antennas at the jammer on Alice's transmission power and consequently on the transmission rate. We consider both cases, one in which the channel knowledge is known and one in which it is unknown by the jammer. We formulate several optimization problems for the transmission strategies of the jammer, to maximize his assistance to Alice, in terms of maximizing a ratio between Willie's and Bob's noise variances. When the channel information is known to the jammer, we show that the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects an optimal tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie. When the channel knowledge is unknown, we show that the optimal strategy of the jammer is either to transmit isotropically to all directions or to the null-space of Bob, where this choice depends on certain channel conditions. This is in contrast to current schemes in the literature. Furthermore, we extend the optimization problems to the case where Bob is also equipped with multiple antennas, and provide insightful results, shown to be asymptotically optimal, accompanied by simulations.

cs.IT↗

arXiv2020

A Macroeconomic SIR Model for COVID-19

The current COVID-19 pandemic and subsequent lockdowns have highlighted the close and delicate relationship between a country's public health and economic health. Macroeconomic models that use preexisting epidemic models to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We develop an SIR model of the COVID-19 pandemic that explicitly considers herd immunity, behavior-dependent transmission rates, remote workers, and indirect externalities of lockdown. This model is presented as an exit time control problem where lockdown ends when the population achieves herd immunity, either naturally or via a vaccine. A social planner prescribes separate levels of lockdown for two separate sections of the adult population: low-risk (ages 20-64) and high-risk (ages 65 and over). These levels are determined via optimization of an objective function which assigns a macroeconomic cost to the level of lockdown and the number of deaths. We find that, by ending lockdowns once herd immunity is reached, high-risk individuals are able to leave lockdown significantly before the arrival of a vaccine without causing large increases in mortality. Moreover, if we incorporate a behavior-dependent transmission rate which represents increased personal caution in response to increased infection levels, both output loss and total mortality are lowered. Lockdown efficacy is further increased when there is less interaction between low- and high-risk individuals, and increased remote work decreases output losses. Overall, our model predicts that a lockdown which ends at the arrival of herd immunity, combined with individual actions to slow virus transmission, can reduce total mortality to one-third of the no-lockdown level, while allowing high-risk individuals to leave lockdown well before vaccine arrival.

physics.soc-ph↗

arXiv2020

Rate of Convergence of the Probability of Ruin in the Cramér-Lundberg Model to its Diffusion Approximation

We analyze the probability of ruin for the {\it scaled} classical Cramér-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart \cite{I1969} to the actuarial literature, amounts to multiplying the Poisson rate $\la$ by $n$, dividing the claim severity by $\sqrtn$, and adjusting the premium rate so that net premium income remains constant. %Therefore, we think of the associated diffusion approximation as being "asymptotic for large values of $\la$." We are the first to use a comparison method to prove convergence of the probability of ruin for the scaled CL process and to derive the rate of convergence. Specifically, we prove a comparison lemma for the corresponding integro-differential equation and use this comparison lemma to prove that the probability of ruin for the scaled CL process converges to the probability of ruin for the limiting diffusion process. Moreover, we show that the rate of convergence for the ruin probability is of order $\mO\big(n^{-1/2}\big)$, and we show that the convergence is {\it uniform} with respect to the surplus. To the best of our knowledge, this is the first rate of convergence achieved for these ruin probabilities, and we show that it is the tightest one in the general case. For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform $\mO\big(n^{-k/2}\big)$ rate of convergence for arbitrary $k \in \N$. We also include two examples that illustrate our results.

math.OC↗

arXiv2020

Private Information Retrieval Over Gaussian MAC

Consider the problem of Private Information Retrieval (PIR), where a user wishes to retrieve a single message from $N$ non-communicating and non-colluding databases (servers). All servers store the same set of $M$ messages and they respond to the user through a block fading Gaussian Multiple Access Channel (MAC). The goal in this setting is to keep the index of the required message private from the servers while minimizing the overall communication overhead. This work provides joint privacy and channel coding retrieval schemes for the Gaussian MAC with and without fading. The schemes exploit the linearity of the channel while using the Compute and Forward (CF) coding scheme. Consequently, single-user encoding and decoding are performed to retrieve the private message. In the case of a channel without fading, the achievable retrieval rate is shown to outperform a separation-based scheme, in which the retrieval and the channel coding are designed separately. Moreover, this rate is asymptotically optimal as the SNR grows, and are up to a constant gap of $2$ bits per channel use from the channel capacity without privacy constraints, for all SNR values. When the channel suffers from fading, the asymmetry between the servers' channels forces a more complicated solution, which involves a hard optimization problem. Nevertheless, we provide coding scheme and lower bounds on the expected achievable retrieval rate which are shown to have the same scaling laws as the channel capacity, both in the number of servers and the SNR.

cs.IT↗

arXiv2020

Compute-and-Forward in Large Relaying Systems: Limitations and Asymptotically Optimal Scheduling

Compute and Forward (CF) is a coding scheme which enables receivers to decode linear combinations of simultaneously transmitted messages while exploiting the linear properties of lattice codes and the additive nature of a shared medium. The scheme was originally designed for relay networks, yet, it was found useful in other communication problems, such as MIMO communication. Works in the current literature assume a fixed number of transmitters and receivers in the system. However, following the increase in communication networks density, it is interesting to investigate the performance of CF when the number of transmitters is large. In this work, we show that as the number of transmitters grows, CF becomes degenerated, in the sense that a relay prefers to decode only one (strongest) user instead of any other linear combination of the transmitted codewords, treating the other users as noise. Moreover, the system's sum-rate tends to zero as well. This makes scheduling necessary in order to maintain the superior abilities CF provides. We thus examine the problem of scheduling for CF. We start with insights on why good scheduling opportunities can be found. Then, we provide an asymptotically optimal, polynomial-time scheduling algorithm and analyze its performance. We conclude that with proper scheduling, CF is not merely non-degenerated, but, in fact, provides a gain for the system sum-rate, up to the optimal scaling law of $O(\log{\log{L}})$.

cs.IT↗

arXiv2020

Privacy-aware Distributed Hypothesis Testing

A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer's observations from those of the detector, given some additional side-information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counterexample that, the strong converse which holds for distributed HT without a privacy constraint, does not hold when a privacy constraint is imposed. This implies that, in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint.

cs.IT↗

arXiv2019

Learning a faceted customer segmentation for discovering new business opportunities at Intel

For sales and marketing organizations within large enterprises, identifying and understanding new markets, customers and partners is a key challenge. Intel's Sales and Marketing Group (SMG) faces similar challenges while growing in new markets and domains and evolving its existing business. In today's complex technological and commercial landscape, there is need for intelligent automation supporting a fine-grained understanding of businesses in order to help SMG sift through millions of companies across many geographies and languages and identify relevant directions. We present a system developed in our company that mines millions of public business web pages, and extracts a faceted customer representation. We focus on two key customer aspects that are essential for finding relevant opportunities: industry segments (ranging from broad verticals such as healthcare, to more specific fields such as 'video analytics') and functional roles (e.g., 'manufacturer' or 'retail'). To address the challenge of labeled data collection, we enrich our data with external information gleaned from Wikipedia, and develop a semi-supervised multi-label, multi-lingual deep learning model that parses customer website texts and classifies them into their respective facets. Our system scans and indexes companies as part of a large-scale knowledge graph that currently holds tens of millions of connected entities with thousands being fetched, enriched and connected to the graph by the hour in real time, and also supports knowledge and insight discovery. In experiments conducted in our company, we are able to significantly boost the performance of sales personnel in the task of discovering new customers and commercial partnership opportunities.

cs.IR↗

arXiv2019

Why Botnets Work: Distributed Brute-Force Attacks Need No Synchronization

In September 2017, McAffee Labs quarterly report estimated that brute force attacks represent 20\% of total network attacks, making them the most prevalent type of attack ex-aequo with browser based vulnerabilities. These attacks have sometimes catastrophic consequences, and understanding their fundamental limits may play an important role in the risk assessment of password-secured systems, and in the design of better security protocols. While some solutions exist to prevent online brute-force attacks that arise from one single IP address, attacks performed by botnets are more challenging. In this paper, we analyze these distributed attacks by using a simplified model. Our aim is to understand the impact of distribution and asynchronization on the overall computational effort necessary to breach a system. Our result is based on Guesswork, a measure of the number of queries (guesses) required of an adversary before a correct sequence, such as a password, is found in an optimal attack. Guesswork is a direct surrogate for time and computational effort of guessing a sequence from a set of sequences with associated likelihoods. We model the lack of synchronization by a worst-case optimization in which the queries made by multiple adversarial agents are received in the worst possible order for the adversary, resulting in a min-max formulation. We show that, even without synchronization, and for sequences of growing length, the asymptotic optimal performance is achievable by using randomized guesses drawn from an appropriate distribution. Therefore, randomization is key for distributed asynchronous attacks. In other words, asynchronous guessers can asymptotically perform brute-force attacks as efficiently as synchronized guessers.

cs.IT↗

arXiv2019

Asymptotic analysis of a multiclass queueing control problem under heavy-traffic with model uncertainty

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions acts to minimize a discounted cost that accounts for the uncertainty. The main result is the asymptotic optimality of a $cμ$-type of policy derived via underlying stochastic differential games studied in [16]. Under this policy, with high probability, rejections are not performed when the workload lies below some cut-off that depends on the ambiguity level. When the workload exceeds this cut-off, rejections are carried out and only from the buffer with the cheapest rejection cost weighted with the mean service rate in some reference model. The allocation part of the policy is the same for all the ambiguity levels. This is the first work to address a heavy-traffic queueing control problem with model uncertainty.

math.PR↗