Publications

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Defender-Attacker Stackelberg games are the foundations of tools deployed for computing optimal patrolling strategies in adversarial domains such as the United states Federal Air Marshals Service and the United States Coast Guard, among others. In Stackelberg game models of these systems the attacker knows only the probability that each target is covered by the defender, but is oblivious to the detailed timing of the coverage schedule. In many real-world situations, however, the attacker can observe the current location of the defender and can exploit this knowledge to reason about the defender's future moves. We study Stackelberg security games in which the defender sequentially moves between targets, with moves constrained by an exogenously specified graph, while the attacker can observe the defender's current location and his (stochastic) policy concerning future moves. We offer five contributions: (1) We model this adversarial patrolling game (APG) as a stochastic game with special structure and present several alternative formulations that leverage the general nonlinear programming (NLP) approach for computing equilibria in zero-sum stochastic games. We show that our formulations yield significantly better solutions than previous approaches. (2) We extend the NLP formulation for APG allow for attacks that may take multiple time steps to unfold. (3) We provide an approximate MILP formulation that uses discrete defender move probabilities. (4) We experimentally demonstrate the efficacy of an NLP-based approach, and systematically study the impact of network topology on the results. (5) We extend our model to allow the defender to construct the graph constraining his moves, at some cost, and offer novel algorithms for this setting, finding that a MILP approximation is much more effective than the exact NLP in this setting. Copyright © 2012, Association for the Advancement of Artificial Intelligence. All rights reserved.

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The goal of this research was to investigate the potential for employing dynamic, decentralized software architectures to achieve reliability in future high-performance computing platforms. These architectures, inspired by peer-to-peer networks such as botnets that already scale to millions of unreliable nodes, hold promise for enabling scientific applications to run usefully on next-generation exascale platforms ({approx} 10{sup 18} operations per second). Traditional parallel programming techniques suffer rapid deterioration of performance scaling with growing platform size, as the work of coping with increasingly frequent failures dominates over useful computation. Our studies suggest that new architectures, in which failures are treated as ubiquitous and their effects are considered as simply another controllable source of error in a scientific computation, can remove such obstacles to exascale computing for certain applications. We have developed a simulation framework, as well as a preliminary implementation in a large-scale emulation environment, for exploration of these 'fault-oblivious computing' approaches. High-performance computing (HPC) faces a fundamental problem of increasing total component failure rates due to increasing system sizes, which threaten to degrade system reliability to an unusable level by the time the exascale range is reached ({approx} 10{sup 18} operations per second, requiring of order millions of processors). As computer scientists seek a way to scale system software for next-generation exascale machines, it is worth considering peer-to-peer (P2P) architectures that are already capable of supporting 10{sup 6}-10{sup 7} unreliable nodes. Exascale platforms will require a different way of looking at systems and software because the machine will likely not be available in its entirety for a meaningful execution time. Realistic estimates of failure rates range from a few times per day to more than once per hour for these platforms. P2P architectures give us a starting point for crafting applications and system software for exascale. In the context of the Internet, P2P applications (e.g., file sharing, botnets) have already solved this problem for 10{sup 6}-10{sup 7} nodes. Usually based on a fractal distributed hash table structure, these systems have proven robust in practice to constant and unpredictable outages, failures, and even subversion. For example, a recent estimate of botnet turnover (i.e., the number of machines leaving and joining) is about 11% per week. Nonetheless, P2P networks remain effective despite these failures: The Conficker botnet has grown to {approx} 5 x 10{sup 6} peers. Unlike today's system software and applications, those for next-generation exascale machines cannot assume a static structure and, to be scalable over millions of nodes, must be decentralized. P2P architectures achieve both, and provide a promising model for 'fault-oblivious computing'. This project aimed to study the dynamics of P2P networks in the context of a design for exascale systems and applications. Having no single point of failure, the most successful P2P architectures are adaptive and self-organizing. While there has been some previous work applying P2P to message passing, little attention has been previously paid to the tightly coupled exascale domain. Typically, the per-node footprint of P2P systems is small, making them ideal for HPC use. The implementation on each peer node cooperates en masse to 'heal' disruptions rather than relying on a controlling 'master' node. Understanding this cooperative behavior from a complex systems viewpoint is essential to predicting useful environments for the inextricably unreliable exascale platforms of the future. We sought to obtain theoretical insight into the stability and large-scale behavior of candidate architectures, and to work toward leveraging Sandia's Emulytics platform to test promising candidates in a realistic (ultimately {ge} 10{sup 7} nodes) setting. Our primary example applications are drawn from linear algebra: a Jacobi relaxation solver for the heat equation, and the closely related technique of value iteration in optimization. We aimed to apply P2P concepts in designing implementations capable of surviving an unreliable machine of 10{sup 6} nodes.