Balancing Asymmetry in Max-sum Using Split Constraint Factor Graphs

Cohen-Lavi, Liel; Zivan, Roie

doi:10.1007/978-3-319-98334-9_43

Cited by 3 publications

(5 citation statements)

References 20 publications

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“…Thus, there exists a damping parameter that guarantees convergence of the algorithm to the optimal solution. This explains the high quality empirical results and fast convergence shown in Cohen and Zivan (2018) for the combination of symmetric splitting and damping.…”

Section: Introductionmentioning

confidence: 60%

“…Theorem 1 and Corollary 2 can help us explain recent empirical results obtained when including both damping and splitting in Max-sum: The results presented by Cohen and Zivan (2018) indicate that damped Max-sum on symmetric SCFGs, converges very fast to high quality solutions. For specific graph structures we can even reach a more specific result: Proposition 1.…”

Section: Max-sum and Bctmentioning

confidence: 72%

“…The SCFG is equivalent to the original factor graph, if the sum of the cost tables of the two functionnodes representing each constraint in the SCFG is equal to the cost table of the single function-node representing the same constraint in the original factor graph. By tuning the similarity between the two function-nodes representing the same constraint one can determine the level of asymmetry in the SCFG (Cohen and Zivan 2018).…”

Section: Split Constraint Factor Graphsmentioning

confidence: 99%

“…As a result, it increases the probability for convergence (Lazic, Frey, and Aarabi 2010;Som and Chockalingam 2010;Tarlow et al 2011;Pretti 2005). Recently, splitting nodes in the factor graph on which belief propagation operates has been shown to be an effective method for triggering convergence of the algorithm, when combined with damping (Ruozzi and Tatikonda 2013;Cohen and Zivan 2018).…”

Section: Introductionmentioning

confidence: 99%

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

Zivan

Lev

Galiki

2020

AAAI

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Belief propagation, an algorithm for solving problems represented by graphical models, has long been known to converge to the optimal solution when the graph is a tree. When the graph representing the problem includes a single cycle, the algorithm either converges to the optimal solution or performs periodic oscillations. While the conditions that trigger these two behaviors have been established, the question regarding the convergence and divergence of the algorithm on graphs that include more than one cycle is still open.Focusing on Max-sum, the version of belief propagation for solving distributed constraint optimization problems (DCOPs), we extend the theory on the behavior of belief propagation in general – and Max-sum specifically – when solving problems represented by graphs with multiple cycles. This includes: 1) Generalizing the results obtained for graphs with a single cycle to graphs with multiple cycles, by using backtrack cost trees (BCT). 2) Proving that when the algorithm is applied to adjacent symmetric cycles, the use of a large enough damping factor guarantees convergence to the optimal solution.

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Section: Introductionmentioning

confidence: 60%

Section: Max-sum and Bctmentioning

confidence: 72%

Section: Split Constraint Factor Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zivan

Lev

Galiki

2020

AAAI

Self Cite

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“…When DCOPs were introduced more than a decade ago, research efforts were initially focused on the investigation of different algorithmic paradigms to solve the problem, including exact search-based methods (Modi et al, 2005;Gershman et al, 2009;Yeoh et al, 2010;Gutierrez et al, 2011), exact inference-based methods (Petcu & Faltings, 2005a;Vinyals et al, 2011), exact declarative methods (Hatano & Hirayama, 2013;Le et al, 2017), approximate search-based methods (Maheswaran et al, 2004a;Zhang et al, 2005;Zivan et al, 2014;Yu et al, 2017;van Leeuwen & Pawelczak, 2017;Chen et al, 2018;Hoang et al, 2018), approximate inference-based methods (Farinelli et al, 2014;Zivan & Peled, 2012;Zivan et al, 2017;Cohen & Zivan, 2018;Cohen et al, 2020;Hoang et al, 2020), and approximate sampling-based methods (Ottens et al, 2017;Nguyen et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Proactive Dynamic Distributed Constraint Optimization Problems

Hoang¹,

Fioretto

Hou

et al. 2022

jair

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The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool for modeling multi-agent coordination problems. To solve DCOPs in a dynamic environment, Dynamic DCOPs (D-DCOPs) have been proposed to model the inherent dynamism present in many coordination problems. D-DCOPs solve a sequence of static problems by reacting to changes in the environment as the agents observe them. Such reactive approaches ignore knowledge about future changes of the problem. To overcome this limitation, we introduce Proactive Dynamic DCOPs (PD-DCOPs), a novel formalism to model D-DCOPs in the presence of exogenous uncertainty. In contrast to reactive approaches, PD-DCOPs are able to explicitly model possible changes of the problem and take such information into account when solving the dynamically changing problem in a proactive manner. The additional expressivity of this formalism allows it to model a wider variety of distributed optimization problems. Our work presents both theoretical and practical contributions that advance current dynamic DCOP models: (i) We introduce Proactive Dynamic DCOPs (PD-DCOPs), which explicitly model how the DCOP will change over time; (ii) We develop exact and heuristic algorithms to solve PD-DCOPs in a proactive manner; (iii) We provide theoretical results about the complexity of this new class of DCOPs; and (iv) We empirically evaluate both proactive and reactive algorithms to determine the trade-offs between the two classes. The final contribution is important as our results are the first that identify the characteristics of the problems that the two classes of algorithms excel in.

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