Worst-case Adversary Research Articles

Adaptive Bundle Methods for Nonlinear Robust Optimization

Currently, there are few theoretical or practical approaches available for general nonlinear robust optimization. Moreover, the approaches that do exist impose restrictive assumptions on the problem structure. We present an adaptive bundle method for nonlinear and nonconvex robust optimization problems with a suitable notion of inexactness in function values and subgradients. As the worst-case evaluation requires a global solution to the adversarial problem, it is a main challenge in a general nonconvex nonlinear setting. Moreover, computing elements of an ε-perturbation of the Clarke subdifferential in the [Formula: see text]-norm sense is in general prohibitive for this class of problems. In this article, instead of developing an entirely new bundle concept, we demonstrate how existing approaches, such as Noll’s bundle method for nonconvex minimization with inexact information [Noll D (2013) Bundle method for non-convex minimization with inexact subgradients and function values. Computational and Analytical Mathematics, Springer Proceedings Mathematics, vol. 50 (Springer, New York), 555–592.] can be modified to be able to cope with this situation. Extending the nonconvex bundle concept to the case of robust optimization in this way, we prove convergence under two assumptions: first, that the objective function is lower C1 and, second, that approximately optimal solutions to the adversarial maximization problem are available. The proposed method is, hence, applicable to a rather general setting of nonlinear robust optimization problems. In particular, we do not rely on a specific structure of the adversary’s constraints. The considered class of robust optimization problems covers the case that the worst-case adversary only needs to be evaluated up to a certain precision. One possibility to evaluate the worst case with the desired degree of precision is the use of techniques from mixed-integer linear programming. We investigate the procedure on some analytic examples. As applications, we study the gas transport problem under uncertainties in demand and in physical parameters that affect pressure losses in the pipes. Computational results for examples in large realistic gas network instances demonstrate the applicability as well as the efficiency of the method. Summary of Contribution: Nonlinear robust optimization is a relevant field of research as real-world optimization problems usually suffer from not precisely known parameters, for example, physical parameters that cannot be measured exactly. Currently, there are few theoretical or practical approaches available for general nonlinear robust optimization. Moreover, the methods that do exist impose restrictive assumptions on the problem structure. Writing nonlinear robust optimization tasks in minimax form, in principle, bundle methods can be used to solve the resulting nonsmooth problem. However, there are a number of difficulties to overcome. First, the inner adversarial problem needs to be solved to global optimality, which is a major challenge in a general nonconvex nonlinear setting. In order to cope with this, an adaptive solution approach, which allows for inexactness, is required. A second challenge is then that the computation of elements from an ε-neighborhood of the Clarke subdifferential is, in general, prohibitive. We show how an existing bundle concept by D. Noll for nonconvex problems with inexactness in function values and subgradients can be adapted to this situation. The resulting method only requires availability of approximate worst-case evaluations, and in particular, it does not rely on a specific structure of the adversarial constraints. To evaluate the worst case with the desired degree of precision, one possibility is the use of techniques from mixed-integer linear programming. In the course of the paper, we discuss convergence properties of the resulting method and demonstrate its efficiency by means of robust gas transport problems.

Game-Theory-Based Consensus Learning of Double-Integrator Agents in the Presence of Worst-Case Adversaries

This work proposes a game-theory-based technique for guaranteeing consensus in unreliable networks by satisfying local objectives. This multi-agent problem is addressed under a distributed framework, in which every agent has to find the best controller against a worst-case adversary so that agreement is reached among the agents in the networked team. The construction of such controllers requires the solution of a system of coupled partial differential equations, which is typically not feasible. The algorithm proposed uses instead three approximators for each agent: one to approximate the value function, one to approximate the control law, and a third one to approximate a worst-case adversary. The tuning laws for every controller and adversary are driven by their neighboring controllers and adversaries, respectively, and neither the controller nor the adversary knows each other’s policies. A Lyapunov stability proof ensures that all the signals remain bounded and consensus is asymptotically reached. Simulation results are provided to demonstrate the efficacy of the proposed approach.

Are Lock-Free Concurrent Algorithms Practically Wait-Free?

Lock-free concurrent algorithms guarantee that some concurrent operation will always make progress in a finite number of steps. Yet programmers prefer to treat concurrent code as if it were wait-free, guaranteeing that all operations always make progress. Unfortunately, designing wait-free algorithms is generally a very complex task, and the resulting algorithms are not always efficient. Although obtaining efficient wait-free algorithms has been a long-time goal for the theory community, most nonblocking commercial code is only lock-free. This article suggests a simple solution to this problem. We show that for a large class of lock-free algorithms, under scheduling conditions that approximate those found in commercial hardware architectures, lock-free algorithms behave as if they are wait-free. In other words, programmers can continue to design simple lock-free algorithms instead of complex wait-free ones, and in practice, they will get wait-free progress. Our main contribution is a new way of analyzing a general class of lock-free algorithms under a stochastic scheduler. Our analysis relates the individual performance of processes to the global performance of the system using Markov chain lifting between a complex per-process chain and a simpler system progress chain. We show that lock-free algorithms are not only wait-free with probability 1 but that in fact a general subset of lock-free algorithms can be closely bounded in terms of the average number of steps required until an operation completes. To the best of our knowledge, this is the first attempt to analyze progress conditions, typically stated in relation to a worst-case adversary, in a stochastic model capturing their expected asymptotic behavior.

Online Optimization Under Adversarial Perturbations

We investigate the problem of online optimization under adversarial perturbations. In each round of this repeated game, a player selects an action from a decision set using a randomized strategy, and then Nature reveals a loss function for this action, for which the player incurs a loss. The game then repeats for a total of $T$ rounds, over which the player seeks to minimize the total incurred loss, or more specifically, the excess incurred loss with respect to a fixed comparison class. The added challenge over traditional online optimization, is that for $k$ of the $T$ rounds, after the player selects an action, an adversarial agent perturbs this action arbitrarily. Through a worst case adversary framework to model the perturbations, we introduce a randomized algorithm that is provably robust against such adversarial attacks. In particular, we show that this algorithm is Hannan consistent with respect to a rich class of randomized strategies under mild regularity conditions.

The Update Complexity of Selection and Related Problems

We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined estimates in form of sub-intervals and the objective is to minimize the number of queries. The previous approaches address the scenario where every query returns an exact value. Our framework is more general as it can deal with a wider variety of inputs and query responses and we establish interesting relationships between them that have not been investigated previously. Although some of the approaches of the previous restricted models can be adapted to the more general model, we require more sophisticated techniques for the analysis and we also obtain improved algorithms for the previous model. We address selection problems in the generalized model and show that there exist 2-update competitive algorithms that do not depend on the lengths or distribution of the sub-intervals and hold against the worst case adversary. We also obtain similar bounds on the competitive ratio for the MST problem in graphs.

Bounded-Contention Coding for the additive network model

Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with \(n\) nodes and at most \(a\) transmitters with information of \(\ell \) bits each within \(O(a\log {n}+a\ell )\) bits of communication with full-duplex radios, and \(O((a\log {n}+a\ell )(\log {n}))\) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within \(O((D+a+\log {n})(a\log {n}+\ell ))\) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.

Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms

In this paper, we study an online make-to-order variant of the classical joint replenishment problem (JRP) that has been studied extensively over the years and plays a fundamental role in broader planning issues, such as the management of supply chains. In contrast to the traditional approaches of the stochastic inventory theory, we study the problem using competitive analysis against a worst-case adversary. Our main result is a 3-competitive deterministic algorithm for the online version of the JRP. We also prove a lower bound of approximately 2.64 on the competitiveness of any deterministic online algorithm for the problem. Our algorithm is based on a novel primal-dual approach using a new linear programming relaxation of the offline JRP model. The primal-dual approach that we propose departs from previous primal-dual and online algorithms in rather significant ways. We believe that this approach can extend the range of problems to which online and primal-dual algorithms can be applied and analyzed.

MINIMAX FILTERING IN WIRELESS SENSOR AND ACTOR NETWORKS

In this paper to handle the mobility of actors a hybrid strategy that includes location updating and location prediction is used. The usage of Kalman Filtering in location prediction high power and energy consumptions. To avoid the drawbacks of Kalman Filtering in location prediction, we make use of Mini max filtering (also Known as H∞ filtering). Mini max Filter has been used in WSANs by minimizing the estimation error and maximizing the worst case adversary noise. Mini max filtering will also minimize power and energy consumptions.

Broadcasting in dynamic radio networks

It is reasonable to claim that almost all major questions related to radio broadcasting can be considered closed as far as static networks are considered: the network never changes during the entire protocol's execution. On the other hand, theoretical results on communication protocols in any scenario where the network topology may change during protocol's execution (i.e. a dynamic radio network) are very few. In this paper, we present a theoretical study of broadcasting in radio networks having dynamic unknown topology. The dynamic network is modeled by means of adversaries: we consider two of them. We first analyze an oblivious, memoryless random adversary that can be seen as the dynamic version of the average-case study presented by Elsässer and Gasieniec in JCSS, 2006. We then consider the deterministic worst-case adversary that, at each time slot, can make any network change (thus the strongest adversary). This is the dynamic version of the worst-case study provided by Bar-Yehuda, Goldreich and Itai in JCSS, 1992. In both cases we provide tight bounds on the completion time of randomized broadcast protocols.

Application of sequential detection schemes for obtaining performance bounds of greedy users in the IEEE 802.11 MAC

The widespread deployment of wireless networks and hot spots that employ the IEEE 802.11 technology has forced network designers to put emphasis on the importance of ensuring efficient and fair use of network resources. In order to be able to evaluate the performance of the adversary, we define a set of security guarantees and requirements for an intrusion detection system and precisely define an adversary model. We then apply the proposed model for defining performance bounds of the worst case adversary and the quickest detection IDS in the IEEE 802.11 MAC.

Performance Bounds for Single Layer Threshold Networks when Tracking a Drifting Adversary

This paper finds upper bounds for the generalization error of three tracking algorithms when confronted with a worst case adversary. A system identification model is used where both the target and tracking network are single layer threshold networks, with the target weights changing slowly (the drift problem). Previous work considered random unbiased drifting adversaries. This paper focuses on the analysis of a worst case drifting adversary. For a small drift rate of γ, we find that upper bounds for the optimal conservative tracker, the perceptron tracker, and the least mean square (LMS) tracker are respectively 2γ/cos(γπ),2γn/πcos(γπ), and γ(2n + 2.5) where n is the number of inputs. Simulation results validate the analysis and also show that the bounds are tight when γ is small for the perceptron and LMS tracker. The effects of additive noise, correlated inputs and non-Gaussian inputs are also discussed. © 1997 Elsevier Science Ltd.