Beyond Trees: Analysis and Convergence of Belief Propagation in Graphs with Multiple Cycles

Zivan, Roie; Lev, Omer; Galiki, Rotem

doi:10.1609/aaai.v34i05.6227

Cited by 10 publications

(18 citation statements)

References 19 publications

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“…DCOPs are traditionally associated with problems in discrete settings (Stranders et al, 2009;Taylor et al, 2010;Zivan et al, 2015;Zivan, Lev, & Galiki, 2020), including DCOP_MST. Attempts to investigate the modeling and solving of DCOPs in continuous domains (e.g., (Voice, Stranders, Rogers, & Jennings, 2010;Hoang, Yeoh, Yokoo, & Rabinovich, 2020;Sarker, Choudhury, & Khan, 2021)), raise challenges concerning, among others, the type of continuous utility/cost functions and the impact of these types on the complexity of the problem.…”

Section: Related Workmentioning

confidence: 99%

“…Different aspects of the Max-sum algorithm have been examined in the literature, focusing on the algorithm's convergence guarantees (Rogers, Farinelli, Stranders, & Jennings, 2011;Zivan et al, 2017Zivan et al, , 2020, evaluation in realistic applications (Ramchurn et al, 2010) and computational complexity (Macarthur et al, 2011;Kim & Lesser, 2013). Our work contributes to this ongoing effort by extending the applicability of Max-sum to teams of mobile sensing agents.…”

Section: Related Workmentioning

confidence: 99%

“…Thus, they act as if they are unary constraints (function-nodes with a single variablenode neighbor) and are not affected by the messages sent to them. According to (Forney et al, 2001;Zivan et al, 2020), Max-sum will converge if and only if the maximal path is consistent. As stated in the observations following Lemmas 2 and 3, unary constraints cannot change the fact that the maximal path in these graphs cannot be inconsistent.…”

Section: Consistent and Inconsistent Pathsmentioning

confidence: 99%

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Collision Avoiding Max-Sum for Mobile Sensor Teams

Pertzovsky,

Zivan,

Agmon

2024

jair

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Recent advances in technology have large teams of robots with limited computation skills work together in order to achieve a common goal. Their personal actions need to contribute to the joint effort, however, they also must assure that they do not harm the efforts of the other members of the team, e.g., as a result of collisions. We focus on the distributed target coverage problem, in which the team must cooperate in order to maximize utility from sensed targets, while avoiding collisions with other agents. State of the art solutions focus on the distributed optimization of the coverage task in the team level, while neglecting to consider collision avoidance, which could have far reaching consequences on the overall performance. Therefore, we propose CAMS: a collision-avoiding version of the Max-sum algorithm, for solving problems including mobile sensors. In CAMS, a factor-graph that includes two types of constraints (represented by function-nodes) is being iteratively generated and solved. The first type represents the task-related requirements, and the second represents collision avoidance constraints. We prove that consistent beliefs are sent by target representing function-nodes during the run of the algorithm, and identify factor-graph structures on which CAMS is guaranteed to converge to an optimal (collision-free) solution. We present an experimental evaluation in extensive simulations, showing that CAMS produces high quality collision-free coverage also in large and complex scenarios. We further present evidence from experiments in a real multi-robot system that CAMS outperforms the state of the art in terms of convergence time.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Consistent and Inconsistent Pathsmentioning

confidence: 99%

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Collision Avoiding Max-Sum for Mobile Sensor Teams

Pertzovsky,

Zivan,

Agmon

2024

jair

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“…A MP algorithm consists of initializing the variables (e.g., at random) and then iterating this set of equations until they converge to a fixed point. In general, convergence may not be mathematically guaranteed; necessary and sufficient conditions for convergence are unclear, but this does not appear to be a significant problem in practice [30,31]. When setting r = 0, these equations reduce to the conventional MP ones.…”

Section: A General Approachmentioning

confidence: 99%

Heterogeneous message passing for heterogeneous networks

Cantwell,

Kirkley,

Radicchi

2023

Phys. Rev. E

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Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally treelike networks but require corrections to maintain their accuracy level in networks rich with short cycles. However, MP may already be computationally challenging on very large networks and additional costs incurred by correcting for cycles could be prohibitive. We show how the issue can be addressed. By allowing each node in the network to have its own level of approximation, one can focus on improving the accuracy of MP approaches in a targeted manner. We perform a systematic analysis of 109 real-world networks and show that our node-based MP approximation is able to increase both the accuracy and speed of traditional MP approaches. We find that, compared to conventional MP, a heterogeneous approach based on a simple heuristic is more accurate in 81% of tested networks, faster in 64% of cases, and both more accurate and faster in 49% of cases.

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“…We consider a step to be an action that starts when a node in the graph received some messages (at least one), performed computation, and ends when it sent some messages (at least one) 4. For an analysis on the size of the damping factor required, with respect to the largest number of neighbors (degree) that a node in the factor graph has, see the work by Zivan et al[15].…”

mentioning

confidence: 99%

The Effect of Asynchronous Execution and Imperfect Communication on Max-sum Belief Propagation

Zivan

Rachmut

Perry

et al. 2023

Preprint

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Max-sum is a version of belief propagation that was adapted for solving distributed constraint optimization problems (DCOPs). It has been studied theoretically and empirically, extended to versions that improve solution quality and converge rapidly, and is applicable to multiple distributed applications. The algorithm was presented both as a synchronous and an asynchronous algorithm, however, neither the differences in the performance of these two execution versions nor the implications of imperfect communication (i.e., massage delay and message loss) on the two versions, have been investigated to the best of our knowledge. We contribute to the body of knowledge on Max-sum by: (1) Establishing the theoretical differences between the two execution versions of the algorithm, focusing on the construction of beliefs; (2) Empirically evaluating the differences between the solutions generated by the two versions of the algorithm, with and without message delay or loss; and (3) Establishing both theoretically and empirically the positive effect of damping on reducing the differences between the two versions. Our results indicate that in contrast to recent published results indicating the drastic effect that message latency has on distributed local search, damped Max-sum is robust to imperfect communication.

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Beyond Trees: Analysis and Convergence of Belief Propagation in Graphs with Multiple Cycles

Cited by 10 publications

References 19 publications

Collision Avoiding Max-Sum for Mobile Sensor Teams

Collision Avoiding Max-Sum for Mobile Sensor Teams

Heterogeneous message passing for heterogeneous networks

The Effect of Asynchronous Execution and Imperfect Communication on Max-sum Belief Propagation

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