The Effect of Asynchronous Execution and Message Latency on Max-Sum

11 Max-sum is a version of belief propagation that was adapted for solving distributed constraint optimization 12 problems (DCOPs). It has been studied theoretically and empirically, extended to versions that improve solution 13 quality and converge rapidly, and is applicable to multiple distributed applications. The algorithm was presented 14 both as a synchronous and an asynchronous algorithm, however, neither the differences in the performance of 15 these two execution versions nor the implications of message latency on the two versions have been investigated 16 to the best of our knowledge. 17 We contribute to the body of knowledge on Max-sum by: (1) Establishing the theoretical differences between 18 the two execution versions of the algorithm, focusing on the construction of beliefs; (2) Empirically evaluating 19 the differences between the solutions generated by the two versions of the algorithm, with and without message 20 latency; and (3) Establishing both theoretically and empirically the positive effect of damping on reducing the 21 differences between the two versions. Our results indicate that in contrast to recent published results indicating 22 the drastic effect that message latency has on distributed local search, damped Max-sum is robust to message 23 latency. 24 2012 ACM Subject Classification Theory of computation → Distributed algorithms; Theory of computation 25 → Constraint and logic programming 26

[1]  Weixiong Zhang,et al.  Distributed stochastic search and distributed breakout: properties, comparison and applications to constraint optimization problems in sensor networks , 2005, Artif. Intell..

[2]  Nicholas R. Jennings,et al.  Decentralised coordination of low-power embedded devices using the max-sum algorithm , 2008, AAMAS.

[3]  Roie Zivan,et al.  Latency-Aware Local Search for Distributed Constraint Optimization , 2021, AAMAS.

[4]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[5]  Yanchen Deng,et al.  Speeding Up Incomplete GDL-based Algorithms for Multi-agent Optimization with Dense Local Utilities , 2020, IJCAI.

[6]  Nicholas R. Jennings,et al.  Decentralised Coordination of Mobile Sensors Using the Max-Sum Algorithm , 2009, IJCAI.

[7]  Amnon Meisels,et al.  Concurrent forward bounding for distributed constraint optimization problems , 2012, Artif. Intell..

[8]  AmewudaAndy Bubune,et al.  Implementation and Evaluation of WLAN 802.11ac for Residential Networks in NS-3 , 2018 .

[9]  Boi Faltings,et al.  A Scalable Method for Multiagent Constraint Optimization , 2005, IJCAI.

[10]  Ziyu Chen,et al.  A class of iterative refined Max-sum algorithms via non-consecutive value propagation strategies , 2018, Autonomous Agents and Multi-Agent Systems.

[11]  Roie Zivan,et al.  Applying Max-sum to asymmetric distributed constraint optimization problems , 2020, Autonomous Agents and Multi-Agent Systems.

[12]  Milind Tambe,et al.  Asynchronous algorithms for approximate distributed constraint optimization with quality bounds , 2010, AAMAS.

[13]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[14]  Gauthier Picard,et al.  Using Message-Passing DCOP Algorithms to Solve Energy-Efficient Smart Environment Configuration Problems , 2016, IJCAI.

[15]  Roie Zivan,et al.  Governing convergence of Max-sum on DCOPs through damping and splitting , 2020, Artif. Intell..

[16]  Nicholas R. Jennings,et al.  Max-sum decentralised coordination for sensor systems , 2008, AAMAS.

[17]  MarinescuRadu,et al.  AND/OR Branch-and-Bound search for combinatorial optimization in graphical models , 2009 .

[18]  Sven Koenig,et al.  BnB-ADOPT: an asynchronous branch-and-bound DCOP algorithm , 2008, AAMAS.

[19]  Steven Okamoto,et al.  Balancing exploration and exploitation in incomplete Min/Max-sum inference for distributed constraint optimization , 2017, Autonomous Agents and Multi-Agent Systems.

[20]  Nicholas R. Jennings,et al.  Agent-based decentralised coordination for sensor networks using the max-sum algorithm , 2014, Autonomous Agents and Multi-Agent Systems.

[21]  G. Forney,et al.  Iterative Decoding of Tail-Biting Trellises and Connections with Symbolic Dynamics , 2001 .

[22]  Yair Weiss,et al.  Correctness of Local Probability Propagation in Graphical Models with Loops , 2000, Neural Computation.

[23]  WeissYair,et al.  Linear Programming Relaxations and Belief Propagation -- An Empirical Study , 2006 .

[24]  Omer Lev,et al.  Beyond Trees: Analysis and Convergence of Belief Propagation in Graphs with Multiple Cycles , 2020, AAAI.

[25]  Makoto Yokoo,et al.  Adopt: asynchronous distributed constraint optimization with quality guarantees , 2005, Artif. Intell..

[26]  Hoong Chuin Lau,et al.  Distributed Gibbs: A Linear-Space Sampling-Based DCOP Algorithm , 2019, J. Artif. Intell. Res..

[27]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[28]  Sekhar Tatikonda,et al.  Message-Passing Algorithms: Reparameterizations and Splittings , 2010, IEEE Transactions on Information Theory.

[29]  Amnon Meisels,et al.  Message delay and DisCSP search algorithms , 2006, Annals of Mathematics and Artificial Intelligence.