ABSTRACTIn many ‘smart city’ applications, congestion arises in part due to the nature of signals received by individuals from a central authority. In the model of , each agent uses one out of multiple resources at each time instant. The per-use cost of a resource depends on the number of concurrent users. A central authority has up-to-date knowledge of the congestion across all resources and uses randomisation to provide a scalar or an interval for each resource at each time. In this paper, the interval to broadcast per resource is obtained by taking the minima and maxima of costs observed within a time window of length r, rather than by randomisation. We show that the resulting distribution of agents across resources also converges in distribution, under plausible assumptions about the evolution of the population over time.
Throughout, we are not aware of any theoretical guarantees on the behavior of policies similar to ours, as described in this paper and @cite_10 . Specifically, we are not aware of any other paper, which would study the broadcasting of intervals, instead of scalars, show its superiority, or study the behaviour of systems, where such signals are being provided. Compared to this paper, the set-up of @cite_10 is much simpler, and so are the proofs and simulations. Unlike @cite_10 , the approach presented in this paper does not employ randomisation, whose use may be unacceptable to the general public, allows for the same signal to be broadcast to all agents, such as at road-side displays, and considers a more elaborate model of the populational response, with risk-aware agents. Both this paper and @cite_10 suggest the importance of the control-theoretic aspects of information provision.
@cite_10
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In the field of infrastructures’ surveillance and protection, it is important to make decisions based on activities occurring in the environment and its local context and conditions. In this paper we use an active rule based event processing architecture in order to make sense of situations from the combination of different signals received by the rule engine. However obtaining some high level information automatically is not without risks, especially in sensitive environments, and detection mistakes can happen for various reasons: the signal’s source can be defective, whether it is human—miss-interpretation of the signal—or computed—material malfunction; the aggregation rules can be wrong syntaxically, for example when a rule will never be triggered or a situation never detected; the interpretation given to the combination of signals does not correspond to the reality on the field—because the knowledge of the rule designer is subjective or because the environment evolves over-time—the rules are therefore incorrect semantically. In this paper, a new approach is proposed to avoid the third kind of error sources. We present a hybrid machine learning technique adapted to the complexity of the rules’ representation, in order to create a system more conform to reality. The proposed approach uses a combination of an Association Rule Mining algorithm and Inductive Logic Programming for rule induction. Empirical studies on simulated datasets demonstrate how our method can contribute to sensible systems such as the security of a public or semi-public place. The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results. We study the question of whether a large population of agents in a traffic network is able to converge to an equilibrium quickly. To that end, we consider a round-based variant of the Wardrop model. Every agent is allowed to reroute its traffic once in a while with the aim of finding a path with minimal latency. As a first result we find that using a replication policy which allows agents to imitate others gives rise to a bicriterial approximate equilibrium very quickly. In particular, the time bound depends logarithmically on the ratio between minimum and maximum latency but is otherwise independent of the network size. In the single-commodity case, this bicriteria approximate equilibrium has an intuitive interpretation as a state in which almost all agents are almost happy. This kind of approximate equilibrium, however, is transient. In order to reach a global approximation, we need to add an exploration component which enables the agents to explore the strategy space independently of the other agents. Although it can be shown that, when used exclusively, exploration policies imply an exponential lower bound, applying exploration carefully allows the population to approximate the global Wardrop equilibrium in polynomial time. Since the distributed and concurrent fashion of our policies bears the risk of oscillating behavior, we must take into account the steepness of the latency functions. We show that the relevant parameter is elasticity, a parameter closely related to the polynomial degree. This improves significantly over earlier results which depend on the absolute slope and therefore have a pseudopolynomial flavor. We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cow-path problem [10, 20, 41, 42], which is relevant for collective foraging in animal groups. In the ANTS problem, k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the two-dimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging, such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. We focus on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if the agents do not commence the search in synchrony, then even initial communication is problematic. This holds, in particular, with respect to the question of whether the agents can communicate and conclude their total number, k. It turns out that the knowledge of k by the individual agents is crucial for performance. Indeed, it is a straightforward observation that the time required for finding the treasure is Ω(D + D2 k), and we show in this paper that this bound can be matched if the agents have knowledge of k up to some constant approximation. We present a tight bound for the competitive penalty that must be paid, in the running time, if the agents have no information about k. Specifically, this bound is slightly more than logarithmic in the number of agents. In addition, we give a lower bound for the setting in which the agents are given some estimation of k. Informally, our results imply that the agents can potentially perform well without any knowledge of their total number k, however, to further improve, they must use some information regarding k. Finally, we propose a uniform algorithm that is both efficient and extremely simple, suggesting its relevance for actual biological scenarios. We present a new stochastic service model with capacity sharing and interruptions, appropriate for the evaluation of the quality of real-time streaming (RTS), like e.g. mobile TV, in wireless cellular networks. The general model takes into account multi-class Markovian process of call arrivals, (to capture different radio channel conditions, requested streaming bit-rates and durations) and allows for a general resource allocation policy saying which users are temporarily denied the requested fixed streaming bit-rates (put in outage) due to resource constraints. We give expressions for several important performance characteristics of the model, including mean time spent in outage and mean number of outage incidents for a typical user of a given class. These expressions involve only stationary probabilities of the (free) traffic demand process, which is a vector of independent Poisson random variables describing the number of users of different classes. In order to analyze RTS in 3GPP Long Term Evolution (LTE) cellular networks, we specify our general model assuming orthogonal user channels with the peak bit-rates close to the theoretical Shannon's bound in the additive white Gaussian noise (AWGN) channel, which leads to the resource constraints in a multi-rate linear form. In this setting we consider a natural class of least-effort-served-first resource allocation policies, for which the characteristics of the model can be further evaluated using Fourier analysis of Poisson variables. Within this class we identify and evaluate an optimal and a fair policy, the latter being suggested by LTE implementations. We also propose some intermediate policies, which allow to solve the optimality fairness tradeoff caused by unequal user radio-channel conditions. Our results can be used for the evaluation of the quality of RTS in LTE networks and dimensioning of these networks. This paper builds upon the scalable admission control schemes for CDMA networks developed in F. (2003, December 2004). These schemes are based on an exact representation of the geometry of both the downlink and the uplink channels and ensure that the associated power allocation problems have solutions under constraints on the maximal power of each station user. These schemes are decentralized in that they can be implemented in such a way that each base station only has to consider the load brought by its own users to decide on admission. By load we mean here some function of the configuration of the users and of their bit rates that is described in the paper. When implemented in each base station, such schemes ensure the global feasibility of the power allocation even in a very large (infinite number of cells) network. The estimation of the capacity of large CDMA networks controlled by such schemes was made in these references. In certain cases, for example for a Poisson pattern of mobiles in an hexagonal network of base stations, this approach gives explicit formulas for the infeasibility probability, defined as the fraction of cells where the population of users cannot be entirely admitted by the base station. In the present paper we show that the notion of infeasibility probability is closely related to the notion of blocking probability, defined as the fraction of users that are rejected by the admission control policy in the long run, a notion of central practical importance within this setting. The relation between these two notions is not bound to our particular admission control schemes, but is of more general nature, and in a simplified scenario it can be identified with the well-known Erlang loss formula. We prove this relation using a general spatial birth-and-death process, where customer locations are represented by a spatial point process that evolves over time as users arrive or depart. This allows our model to include the exact representation of the geometry of inter-cell and intra-cell interferences, which play an essential role in the load indicators used in these cellular network admission control schemes. Humans are experts at high-fidelity imitation -- closely mimicking a demonstration, often in one attempt. Humans use this ability to quickly solve a task instance, and to bootstrap learning of new tasks. Achieving these abilities in autonomous agents is an open problem. In this paper, we introduce an off-policy RL algorithm (MetaMimic) to narrow this gap. MetaMimic can learn both (i) policies for high-fidelity one-shot imitation of diverse novel skills, and (ii) policies that enable the agent to solve tasks more efficiently than the demonstrators. MetaMimic relies on the principle of storing all experiences in a memory and replaying these to learn massive deep neural network policies by off-policy RL. This paper introduces, to the best of our knowledge, the largest existing neural networks for deep RL and shows that larger networks with normalization are needed to achieve one-shot high-fidelity imitation on a challenging manipulation task. The results also show that both types of policy can be learned from vision, in spite of the task rewards being sparse, and without access to demonstrator actions. We consider the generalized dirty-paper channel Y=X+S+N,E X sup 2 spl les P sub X , where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P sub X , these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1 2log(2 spl pi e 12) spl ap 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1 2log2 spl pi eG( spl Lambda ), where G( spl Lambda ) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels. This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R's equilibrium expected utility rises when agents' preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents' preferences are more similar. In this work we present a new agent architecture, called Reactor, which combines multiple algorithmic and architectural contributions to produce an agent with higher sample-efficiency than Prioritized Dueling DQN (, 2016) and Categorical DQN (, 2017), while giving better run-time performance than A3C (, 2016). Our first contribution is a new policy evaluation algorithm called Distributional Retrace, which brings multi-step off-policy updates to the distributional reinforcement learning setting. The same approach can be used to convert several classes of multi-step policy evaluation algorithms designed for expected value evaluation into distributional ones. Next, we introduce the eta -leave-one-out policy gradient algorithm which improves the trade-off between variance and bias by using action values as a baseline. Our final algorithmic contribution is a new prioritized replay algorithm for sequences, which exploits the temporal locality of neighboring observations for more efficient replay prioritization. Using the Atari 2600 benchmarks, we show that each of these innovations contribute to both the sample efficiency and final agent performance. Finally, we demonstrate that Reactor reaches state-of-the-art performance after 200 million frames and less than a day of training. Selective families, a weaker variant of superimposed codes [KS64, F92, 197, CR96], have been recently used to design Deterministic Distributed Broadcast (DDB) protocols for unknown radio networks (a radio network is said to be unknown when the nodes know nothing about the network but their own label) [CGGPR00, CGOR00]. We first provide a general almost tight lower bound on the size of selective families. Then, by reverting the selective families - DDB protocols connection, we exploit our lower bound to construct a family of “hard” radio networks (i.e. directed graphs). These networks yield an O(n log D) lower bound on the completion time of DDB protocols that is superlinear (in the size n of the network) even for very small maximum eccentricity D of the network, while all the previous lower bounds (e.g. O(D log n) [CGGPR00]) are superlinear only when D is almost linear. On the other hand, the previous upper bounds are all superlinear in n independently of the eccentricity D and the maximum in-degree d of the network. We introduce a broadcast technique that exploits selective families in a new way. Then, by combining selective families of almost optimal size with our new broadcast technique, we obtain an O(Dd log3 n) upper bound that we prove to be almost optimal when d = O(n D). This exponentially improves over the best known upper bound [CGR00) when D, d = O(polylogn). Furthermore, by comparing our deterministic upper bound with the best known randomized one [BGI87] we obtain a new, rather surprising insight into the real gap between deterministic and randomized protocols. It turns out that this gap is exponential (as discovered in [BGI87]), but only when the network has large maximum in-degree (i.e. d = O(na), for some constant a > O). We then look at the multibroadcast problem on unknown radio networks. A similar connection to that between selective families and (single) broadcast also holds between superimposed codes and multibroadcast. We in fact combine a variant of our (single) broadcast technique with superimposed codes of almost optimal size available in literature [EFF85, HS87, I97, CHI99]. This yields a multibroadcast protocol having completion time O(Dd2 log3 n). Finally, in order to determine the limits of our multibroadcast technique, we generalize (and improve) the best known lower bound [CR96] on the size of superimposed codes. We consider networks consisting of nodes with radios, and without any wired infrastructure, thus necessitating all communication to take place only over the shared wireless medium. The main focus of this paper is on the effect of fading in such wireless networks. We examine the attenuation regime where either the medium is absorptive, a situation which generally prevails, or the path loss exponent is greater than 3. We study the transport capacity, defined as the supremum over the set of feasible rate vectors of the distance weighted sum of rates. We consider two assumption sets. Under the first assumption set, which essentially requires only a mild time average type of bound on the fading process, we show that the transport capacity can grow no faster than O(n), where n denotes the number of nodes, even when the channel state information (CSI) is available noncausally at both the transmitters and the receivers. This assumption includes common models of stationary ergodic channels; constant, frequency-selective channels; flat, rapidly varying channels; and flat slowly varying channels. In the second assumption set, which essentially features an independence, time average of expectation, and nonzeroness condition on the fading process, we constructively show how to achieve transport capacity of spl Omega (n) even when the CSI is unknown to both the transmitters and the receivers, provided that every node has an appropriately nearby node. This assumption set includes common models of independent and identically distributed (i.i.d.) channels; constant, flat channels; and constant, frequency-selective channels. The transport capacity is achieved by nodes communicating only with neighbors, and using only point-to-point coding. The thrust of these results is that the multihop strategy, toward which much protocol development activity is currently targeted, is appropriate for fading environments. The low attenuation regime is open. We define and analyze a random coverage process of the @math -dimensional Euclidian space which allows one to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Johnson-Mehl model. Like for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidian space and a sequence of real valued random variables considered as marks of this point process. In this coverage process, the cell attached to a point is defined as the region of the space where the effect of the mark of this point exceeds an affine function of the cumulated effect of all marks. This cumulated effect is defined as the shot noise process associated with the marked point process. In addition to analyzing and visualizing this continuum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyze convergence properties of the coverage process using the framework of closed sets, and its differentiability properties using perturbation analysis. Our results require a pathwise continuity property for the shot noise process for which we provide sufficient conditions. The model in question stems from wireless communications where several antennas share the same (or different but interfering) channel(s). In this case, the area where the signal of a given antenna can be received is the area where the signal to interference ratio is large enough. We describe this class of problems in detail in the paper. The obtained results allow one to compute quantities of practical interest within this setting: for instance the outage probability is obtained as the complement of the volume fraction; the law of the number of cells covering a point allows one to characterize handover strategies etc. We introduce autonomous gossiping (A G), a new genre epidemic algorithm for selective dissemination of information in contrast to previous usage of epidemic algorithms which flood the whole network. A G is a paradigm which suits well in a mobile ad-hoc networking (MANET) environment because it does not require any infrastructure or middleware like multicast tree and (un)subscription maintenance for publish subscribe, but uses ecological and economic principles in a self-organizing manner in order to achieve any arbitrary selectivity (flexible casting). The trade-off of using a stateless self-organizing mechanism like A G is that it does not guarantee completeness deterministically as is one of the original objectives of alternate selective dissemination schemes like publish subscribe. We argue that such incompleteness is not a problem in many non-critical real-life civilian application scenarios and realistic node mobility patterns, where the overhead of infrastructure maintenance may outweigh the benefits of completeness, more over, at present there exists no mechanism to realize publish subscribe or other paradigms for selective dissemination in MANET environments. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. We begin by developing tight lower and upper bounds on the runtime of the algorithm described above. First, it is shown that on ?-regular graphs this algorithm requires at least log2?1?n+log(???1)?n?o(logn)?1.69log2n rounds to inform all n nodes. Together with a result of Pittel B. Pittel, On spreading a rumor, SIAM Journal on Applied Mathematics, 47 (1) (1987) 213?223 this bound implies that the algorithm has the best performance on complete graphs among all regular graphs. For general graphs, we prove a slightly weaker lower bound of log2?1?n+log4n?o(logn)?1.5log2n, where ? denotes the maximum degree of G. We also prove two general upper bounds, (1+o(1))nlnn and O(n??), respectively, where ? denotes the minimum degree.The second part of this paper is devoted to the analysis of fault-tolerance. We show that if the informed nodes are allowed to fail in some step with probability 1?p, then the broadcasting time increases by at most a factor 6 p. As a by-product, we determine the performance of agent based broadcasting in certain graphs and obtain bounds for the runtime of randomized broadcasting on Cartesian products of graphs. Consider two parties who wish to communicate in order to execute some interactive protocol π. However, the communication channel between them is noisy: An adversary sees everything that is transmitted over the channel and can change a constant fraction of the bits arbitrarily, thus interrupting the execution of π (which was designed for an error-free channel). If π only contains a single long message, then a good error correcting code would overcome the noise with only a constant overhead in communication. However, this solution is not applicable to interactive protocols consisting of many short messages. Schulman [1992, 1993] introduced the notion of interactive coding: A simulator that, given any protocol π, is able to simulate it (i.e., produce its intended transcript) even in the presence of constant rate adversarial channel errors, and with only constant (multiplicative) communication overhead. However, the running time of Schulman's simulator, and of all simulators that followed, has been exponential (or subexponential) in the communication complexity of π (which we denote by N). In this work, we present three efficient simulators, all of which are randomized and have a certain failure probability (over the choice of coins). The first runs in time poly(N), has failure probability roughly 2-N, and is resilient to 1 32-fraction of adversarial error. The second runs in time O(N log N), has failure probability roughly 2-N, and is resilient to some constant fraction of adversarial error. The third runs in time O(N), has failure probability 1 poly(N), and is resilient to some constant fraction of adversarial error. (Computational complexity is measured in the RAM model.) The first two simulators can be made deterministic if they are a priori given a random string (which may be known to the adversary ahead of time). In particular, the simulators can be made to be nonuniform and deterministic (with equivalent performance). The fundamental problem of multiple secondary users contending for opportunistic spectrum access over multiple channels in cognitive radio networks has been formulated recently as a decentralized multi-armed bandit (D-MAB) problem. In a D-MAB problem there are @math users and @math arms (channels) that each offer i.i.d. stochastic rewards with unknown means so long as they are accessed without collision. The goal is to design a decentralized online learning policy that incurs minimal regret, defined as the difference between the total expected rewards accumulated by a model-aware genie, and that obtained by all users applying the policy. We make two contributions in this paper. First, we consider the setting where the users have a prioritized ranking, such that it is desired for the @math -th-ranked user to learn to access the arm offering the @math -th highest mean reward. For this problem, we present the first distributed policy that yields regret that is uniformly logarithmic over time without requiring any prior assumption about the mean rewards. Second, we consider the case when a fair access policy is required, i.e., it is desired for all users to experience the same mean reward. For this problem, we present a distributed policy that yields order-optimal regret scaling with respect to the number of users and arms, better than previously proposed policies in the literature. Both of our distributed policies make use of an innovative modification of the well known UCB1 policy for the classic multi-armed bandit problem that allows a single user to learn how to play the arm that yields the @math -th largest mean reward. The paper studies broadcasting in radio networks whose stations are represented by points in the Euclidean plane. In any given time step, a station can either receive or transmit. A message transmitted from station (v) is delivered to every station (u) at distance at most (1) from (v), but (u) successfully hears the message if and only if (v) is the only station at distance at most (1) from (u) that transmitted in this time step. A designated source station has a message that should be disseminated throughout the network. All stations other than the source are initially idle and wake up upon the first time they hear the source message. It is shown in [11] that the time complexity of broadcasting depends on two parameters of the network, namely, its diameter (in hops) (D) and a lower bound (d) on the Euclidean distance between any two stations. The inverse of (d) is called the granularity of the network, denoted by (g). Specifically, the authors of [11] present a broadcasting algorithm that works in time (O (D g)) and prove that every broadcasting algorithm requires Ω (D √g) time. In this paper, we distinguish between the arbitrary deployment setting, originally studied in [11], in which stations can be placed everywhere in the plane, and the new grid deployment setting, in which stations are only allowed to be placed on a (d)-spaced grid. Does the latter (more restricted) setting provides any speedup in broadcasting time complexity? Although the (O (D g)) broadcasting algorithm of [11] works under the (original) arbitrary deployment setting, it turns out that the Ω (D √g) lower bound remains valid under the grid deployment setting. Still, the above question is left unanswered. The current paper answers this question affirmatively by presenting a provable separation between the two deployment settings. We establish a tight lower bound on the time complexity of broadcasting under the arbitrary deployment setting proving that broadcasting cannot be completed in less than Ω ( D √g) time. For the grid deployment setting, we develop a broadcasting algorithm that runs in time O ( D g5 6 log g), thus breaking the linear dependency on (g). This paper characterizes the performance in terms of queueing stability of a network composed of multiple MIMO transmitter-receiver pairs taking into account the dynamic traffic pattern and the probing feedback cost. We adopt a centralized scheduling scheme that selects a number of active pairs in each time-slot. We consider that the transmitters apply interference alignment (IA) technique if two or more pairs are active, whereas in the special case where one pair is active point-to-point MIMO singular value decomposition (SVD) is used. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case we provide a centralized probing policy that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system, where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we provide the conditions under which IA yields a queueing stability gain compared to SVD. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate numbers of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided. Consider two parties Alice and Bob, who hold private inputs x and y, and wish to compute a function f(x, y) privately in the information theoretic sense; that is, each party should learn nothing beyond f(x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f(x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties' inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant c > 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors. The same impossibility holds also for sub-constant noise rate, e.g., when c is exponentially small (as a function of the input size).