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When showing your hand pays off: Announcing strategic intentions in Colonel Blotto games

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arXiv 2020年

作者： Chandan, Rahul Paarporn, Keith Marden, Jason R. Department of Electrical and Computer Engineering Center of Control Dynamical Systems and Computation UC SantaBarbara United States

— In competitive adversarial environments, it is often advantageous to obfuscate one’s strategies or capabilities. However, revealing one’s strategic intentions may shift the dynamics of the competition in complex ways. Can it ever be advantageous to reveal strategic intentions to an opponent? In this paper, we consider three-stage Colonel Blotto games in which one player can choose whether or not to pre-commit resources to a single battlefield before play begins. This pre-commitment is public knowledge. In response, the opponent can either secure the battlefield by matching the pre-commitment with its own forces, or withdraw. In a two-player setting, we show that a weaker player never has an incentive to pre-commit any amount of resources to a battlefield regardless of how valuable it is. We then consider a three-player setting in which two players fight against a common adversary on separate fronts. Only one of the two players facing the adversary has the option of pre-committing. We find there are instances where this player benefits from pre-committing. The analysis indicates that under non-cooperative team settings and no possibility of forming alliances, there can be incentives to publicly announce one’s strategic intentions to an adversary. Copyright © 2020, The Authors. All rights reserved.

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Robust implicit networks via non-euclidean contractions 21

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Robust implicit networks via non-euclidean contractions

Proceedings of the 35th International Conference on Neural Information Processing systems

作者： Saber Jafarpour Alexander Davydov Anton V. Proskurnikov Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Department of Electronics and Telecommunications Politecnico di Torino Turin Italy and Institute for Problems in Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia

ISBN: (纸本)9781713845393

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are equivalent to infinite-depth weight-tied feedforward networks. While implicit models show improved accuracy and significant reduction in memory consumption, they can suffer from ill-posedness and convergence *** paper provides a new framework, which we call Non-Euclidean Monotone Operator Network (NEMON), to design well-posed and robust implicit neural networks based upon contraction theory for the non-Euclidean norm ℓ∞. Our framework includes (i) a novel condition for well-posedness based on one-sided Lipschitz constants, (ii) an average iteration for computing fixed-points, and (iii) explicit estimates on input-output Lipschitz constants. Additionally, we design a training problem with the well-posedness condition and the average iteration as constraints and, to achieve robust models, with the input-output Lipschitz constant as a regularizer. Our ℓ∞ well-posedness condition leads to a larger polytopic training search space than existing conditions and our average iteration enjoys accelerated convergence. Finally, we evaluate our framework in image classification through the MNIST and the CIFAR-10 datasets. Our numerical results demonstrate improved accuracy and robustness of the implicit models with smaller input-output Lipschitz bounds.

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Broadcasting solutions on networked systems of phase oscillators

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arXiv 2022年

作者： Nguyen, Tung T. Budzinski, Roberto C. Pasini, Federico W. Delabays, Robin Mináč, Ján Muller, Lyle E. Department of Mathematics Western University LondonON Canada Western Academy for Advanced Research Western University LondonON Canada Western Institute for Neuroscience Western University LondonON Canada University of Applied Sciences and Arts of Western Switzerland HES-SO Sion Switzerland Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA United States

Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more realistic and rich modeling option. On the other hand, it can lead to intrinsic difficulty in analyzing the system. Here, we present an approach to investigate the dynamics of Kuramoto oscillators on networks with different levels of connections: a network of networks. To do so, we utilize a construction in network theory known as the join of networks, which represents "intra-area" and "inter-area" connections. This approach provides a reduced representation of the original, multi-level system, where both systems have equivalent dynamics. Then, we can find solutions for the reduced system and broadcast them to the original network of networks. Moreover, using the same idea we can investigate the stability of these states, where we can obtain information on the Jacobian of the multi-level system by analyzing the reduced one. This approach is general for arbitrary connection schemes between nodes within the same area. Finally, our work opens the possibility of studying the dynamics of networked systems using a simpler representation, thus leading to a better understanding of the dynamical behavior of these systems. © 2022, CC BY.

关键词： Dynamics

Markov chain-based stochastic strategies for robotic surveillance

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arXiv 2020年

作者： Duan, Xiaoming Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where the efficiency is defined with respect to relevant underlying performance metrics. We first start by reviewing the basics of Markov chains, which is the primary motion model for stochastic robotic surveillance. Then two main criteria regarding the speed and unpredictability of surveillance strategies are discussed. The central objects that appear throughout the treatment is the hitting times of Markov chains, their distributions and expectations. We formulate various optimization problems based on the concerned metrics in different scenarios and establish their respective properties. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Topology inference with multivariate cumulants: The Möbius Inference Algorithm

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arXiv 2020年

作者： Smith, Kevin D. Jafarpour, Saber Swami, Ananthram Bullo, Francesco Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States Army Research Laboratory

Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology. However, the standard approach to topology mapping-namely, active probing with traceroutes-relies on cooperation from increasingly non-cooperative routers, leading to missing information. Network tomography, which uses end-to-end measurements of additive link metrics (like delays or log packet loss rates) across monitor paths, is a possible remedy. Network tomography does not require that routers cooperate with traceroute probes, and it has already been used to infer the structure of multicast trees. This paper goes a step further. We provide a tomographic method to infer the underlying routing topology of an arbitrary set of monitor paths using the joint distribution of end-to-end measurements, without making any assumptions on routing behavior. Our approach, called the Möbius Inference Algorithm (MIA), uses cumulants of this distribution to quantify high-order interactions among monitor paths, and it applies Möbius inversion to "disentangle" these interactions. In addition to MIA, we provide a more practical variant called Sparse Möbius Inference, which uses various sparsity heuristics to reduce the number and order of cumulants required to be estimated. We show the viability of our approach using synthetic case studies based on real-world ISP topologies. Copyright © 2020, The Authors. All rights reserved.

关键词： Topology

Stochastic strategies for robotic surveillance as stackelberg games

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arXiv 2020年

作者： Duan, Xiaoming Paccagnan, Dario Bullo, Francesco Mechanical Engineering Department the Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it knows the current location of the mobile agent and can learn the surveillance strategy. The goal for the mobile robot is to design a stochastic strategy so as to maximize the probability of capturing the intruder. We model the strategic interactions between the surveillance robot and the intruder as a Stackelberg game, and optimal and suboptimal Markov chain based surveillance strategies in star, complete and line graphs are studied. We first derive a universal upper bound on the capture probability, i.e., the performance limit for the surveillance agent. We show that this upper bound is tight in the complete graph and further provide suboptimality guarantees for a natural design. For the star and line graphs, we first characterize dominant strategies for the surveillance agent and the intruder. Then, we rigorously prove the optimal strategy for the surveillance agent. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Robust Implicit Networks via Non-Euclidean Contractions

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arXiv 2021年

作者： Jafarpour, Saber Davydov, Alexander Proskurnikov, Anton V. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States Department of Electronics and Telecommunications Politecnico di Torino Turin Italy Institute for Problems in Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are equivalent to infinite-depth weight-tied feedforward networks. While implicit models show improved accuracy and significant reduction in memory consumption, they can suffer from ill-posedness and convergence instability. This paper provides a new framework, which we call Non-Euclidean Monotone Operator Network (NEMON), to design well-posed and robust implicit neural networks based upon contraction theory for the non-Euclidean norm ∞. Our framework includes (i) a novel condition for well-posedness based on one-sided Lipschitz constants, (ii) an average iteration for computing fixed-points, and (iii) explicit estimates on input-output Lipschitz constants. Additionally, we design a training problem with the well-posedness condition and the average iteration as constraints and, to achieve robust models, with the input-output Lipschitz constant as a regularizer. Our ∞ well-posedness condition leads to a larger polytopic training search space than existing conditions and our average iteration enjoys accelerated convergence. Finally, we evaluate our framework in image classification through the MNIST and the CIFAR-10 datasets. Our numerical results demonstrate improved accuracy and robustness of the implicit models with smaller input-output Lipschitz bounds. Code is available at https://***/davydovalexander/Non-Euclidean_Mon_Op_Net. Copyright © 2021, The Authors. All rights reserved.

关键词： computation theory

Assign and appraise: Achieving optimal performance in collaborative teams

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arXiv 2020年

作者： Huang, Elizabeth Y. Paccagnan, Dario Mei, Wenjun Bullo, Francesco Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106-5070 United States Automatic Control Laboratory ETH Zurich8092 Switzerland

Tackling complex team problems requires understanding each team member’s skills in order to devise a task assignment maximizing the team performance. This paper proposes a novel quantitative model describing the decentralized process by which individuals in a team learn who has what abilities, while concurrently assigning tasks to each of the team members. In the model, the appraisal network represents team member’s evaluations of one another and each team member chooses their own workload. The appraisals and workload assignment change simultaneously: each member builds their own local appraisal of neighboring members based on the performance exhibited on previous tasks, while the workload is redistributed based on the current appraisal estimates. We show that the appraisal states can be reduced to a lower dimension due to the presence of conserved quantities associated to the cycles of the appraisal network. Building on this, we provide rigorous results characterizing the ability, or inability, of the team to learn each other’s skill and thus converge to an allocation maximizing the team performance. We complement our analysis with extensive numerical experiments. Copyright © 2020, The Authors. All rights reserved.

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Rethinking the Micro-Foundation of Opinion Dynamics: Rich Consequences of an Inconspicuous Change 3rd

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Rethinking the Micro-Foundation of Opinion Dynamics: Rich Co...

3rd IFAC Workshop on Cyber-Physical and Human systems, CPHS 2020

作者： Mei, Wenjun Bullo, Francesco Chen, Ge Hendrickx, Julien M. Dörfler, Florian Automatic Control Laboratory Eth Zurich Zurich8006 Switzerland Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Academy of Mathematics and Systems Science Chinese Academy of Science Beijing100190 China Institute of Information and Communication Technologies Electronics and Applied Mathematics Université Catholique de Louvain Louvain-la-NeuveB-1348 Belgium Automatic Control Laboratory Eth Zurich Zurich8006 Switzerland

Mathematical modeling plays a fundamental role in understanding how social influence shapes individuals' opinions. Although most opinion dynamics models assume that individuals update their opinions by averaging others' opinions, we point out that the weighted-averaging mechanism features a non-negligible unrealistic implication. We propose a new micro-foundation of opinion dynamics, i.e., the weighted-median mechanism, in the framework of cognitive dissonance theory and resolves the shortcomings of weighted averaging. Validation via empirical data indicates that the weighted-median mechanism significantly outperforms the weighted-averaging mechanism in predicting individual opinion shifts. Compared with the averaging-based opinion dynamics, the weighted-median model, despite its simplicity in form, replicates more realistic features of opinion dynamics, and exhibits richer phase-transition behavior depending on more delicate and robust network structures. The novel weighted-median model opens up a new line of research and renovates our understanding of the opinion formation process. ©2020 The *** is an open access article under the CC BY-NC-ND license.

关键词： Multi agent systems