Resilient monotone submodular function maximization

Tzoumas, Vasileios; Gatsis, Konstantinos; Jadbabaie, Ali; Pappas, George J.

doi:10.1109/cdc.2017.8263844

Cited by 39 publications

(43 citation statements)

References 30 publications

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“…To quantify the algorithm's approximation performance, we exploited a notion of curvature for monotone (not necessarily submodular) set functions, and contributed a first step towards characterizing the curvature's effect on the approximability of resilient sequential maximization. Our curvature-dependent characterizations complement the current knowledge on the curvature's effect on the approximability of simpler problems, such as of non-sequential resilient maximization [22], [23], and of nonresilient maximization [17], [18], [20]. Finally, we supported our theoretical analyses with simulated experiments.…”

Section: Concluding Remarks and Future Worksupporting

confidence: 74%

Resilient Monotone Sequential Maximization

Tzoumas

Jadbabaie

Pappas

2018

2018 IEEE Conference on Decision and Control (CDC)

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Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and actuators fail. Thence, traditional sequential design paradigms become insufficient and, in contrast, resilient sequential designs that adapt against system-wide attacks, deletions, or failures become important. In general, resilient sequential design problems are computationally hard. Also, even though they often involve objective functions that are monotone and (possibly) submodular, no scalable approximation algorithms are known for their solution. In this paper, we provide the first scalable algorithm, that achieves the following characteristics: system-wide resiliency, i.e., the algorithm is valid for any number of denial-ofservice attacks, deletions, or failures; adaptiveness, i.e., at each time step, the algorithm selects system elements based on the history of inflicted attacks, deletions, or failures; and provable approximation performance, i.e., the algorithm guarantees for monotone objective functions a solution close to the optimal. We quantify the algorithm's approximation performance using a notion of curvature for monotone (not necessarily submodular) set functions. Finally, we support our theoretical analyses with simulated experiments, by considering a control-aware sensor scheduling scenario, namely, sensing-constrained robot navigation.

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Section: Concluding Remarks and Future Worksupporting

confidence: 74%

Resilient Monotone Sequential Maximization

Tzoumas

Jadbabaie

Pappas

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…These benefits have drawn attention in many different contexts [2]- [4]. Sample applications include sensor selection [5], detection [6], resource allocation [7], active learning [8], interpretability of neural networks (NNs) [9], and adversarial attacks [10].…”

Section: Submodularity: a Useful Property For Optimizationmentioning

confidence: 99%

Submodularity in Action: From Machine Learning to Signal Processing Applications

Tohidi

Amiri

Coutiño

et al. 2020

IEEE Signal Process. Mag.

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ubmodularity is a discrete domain functional property that can be interpreted as mimicking the role of well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners, as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: 1) relaxation into the continuous domain to obtain an approximate solution or 2) the development of a tailored algorithm that applies directly in the discrete domain. In both approaches, worst-case performance guarantees are often hard to establish. Furthermore, they are often complex and thus not practical for large-scale problems. In this article, we show how certain scenarios lend themselves to exploiting submodularity for constructing scalable solutions with provable worst-case performance guarantees. We introduce a variety of submodular-friendly applications and elucidate the relation of submodularity to convexity and concavity, which enables efficient optimization. With a mixture of theory and practice, we present different flavors of submodularity accompanying illustrative real-world case studies from modern SP and ML. In all of the cases, optimization algorithms are presented along with hints on how optimality guarantees can be established.

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“…To prove the part 1 − κ J of the bound in the right-handside of ineq. (11), we follow the steps of the proof of [22,Theorem 1], and make the following observations:…”

Section: A Proof Of Theorem 1's Part 1 (Approximation Performance)mentioning

confidence: 99%

“…However, [21]- [23] focus on the resilient selection of a small subset of elements in the event of attacks or failures, whereas the information acquisition problem requires the selection of controls for all robots over a time horizon. In this paper, we capitalize on the recent results in [22], [23] and seek to bridge the gap between developments in set function optimization and robotic control design to enable critical missions necessitating resilient active information gathering with mobile robots.…”

Section: Introductionmentioning

confidence: 99%

“…, b |B| }. f (A) + |B| i=1 f (b i ) ≥ (1 − c f )f (A) + |B| i=1 f (b i ))(27)≥ (1 − c f )f (A ∪ {b 1 }) + |B| i=2 f (b i ) ≥ (1 − c f )f (A ∪ {b 1 , b 2 }) + c f )f (A ∪ B),where(27) holds since 0 ≤ c f ≤ 1, and the rest due to Lemma 4 since A ∩ B = ∅ implies A \ {b 1 } = ∅, generality) J is non-negative and J(∅) = 0, then: J(u 1:n ) ≤ J(u 1:n ) + i−1 , u i+1,n })(36)…”

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confidence: 99%

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Resilient Active Information Gathering with Mobile Robots

Schlotfeldt

Tzoumas

Thakur

et al. 2018

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Applications in robotics, such as multi-robot target tracking, involve the execution of information acquisition tasks by teams of mobile robots. However, in failure-prone or adversarial environments, robots get attacked, their communication channels get jammed, and their sensors fail, resulting in the withdrawal of robots from the collective task, and, subsequently, the inability of the remaining active robots to coordinate with each other. As a result, traditional design paradigms become insufficient and, in contrast, resilient designs against system-wide failures and attacks become important. In general, resilient design problems are hard, and even though they often involve objective functions that are monotone and (possibly) submodular, scalable approximation algorithms for their solution have been hitherto unknown. In this paper, we provide the first algorithm, enabling the following capabilities: minimal communication, i.e., the algorithm is executed by the robots based only on minimal communication between them; system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks and failures; and provable approximation performance, i.e., the algorithm ensures for all monotone and (possibly) submodular objective functions a solution that is finitely close to the optimal. We support our theoretical analyses with simulated and realworld experiments, by considering an active information acquisition application scenario, namely, multi-robot target tracking. ).This research is partially supported by ARL CRA DCIST W911NF-17-2-0181 and the Rockefeller Foundation.• (Problem definition) We formalize the problem of resilient active information gathering with mobile robots against multi-robot denial-of-service attacks or failures. arXiv:1803.09730v3 [cs.RO] 2 Sep 2018 APPENDIX A PRELIMINARY LEMMAS AND DEFINITIONSNotation. In the appendix we use the following notation to support the proofs in this paper: in particular, consider a finite ground set V and a set function f : 2 V → R. Then, for any set X ⊆ V and any set X ⊆ V, the symbol f (X |X ) denotes the marginal value f (X ∪ X ) − f (X ). Moreover, the symbol κ f is the total curvature of f (Definition 3), and the symbol c f is the total curvature of f (Definition 4).This appendix contains lemmas that will support the proof of Theorem 1 in this paper; moreover, it contains a generalized description of the algorithm coordinate descent [20, Section IV] (to any non-decreasing information objective function in the active robot set), and a lemma, which will support the proof of Proposition 1 in this paper.

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Resilient monotone submodular function maximization

Cited by 39 publications

References 30 publications

Resilient Monotone Sequential Maximization

Resilient Monotone Sequential Maximization

Submodularity in Action: From Machine Learning to Signal Processing Applications

Resilient Active Information Gathering with Mobile Robots

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