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Bregman Consensus

  • Andrei N. Soklakov
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Abstract

Consider a community of agents who are seeking consensus on a set of parameters. The agents agree to use the same Bregman-type divergence to quantify disagreement between their individual estimates of the parameters but have varying confidence in each other's abilities. Each agent is happy to revise their estimate by moving to the weighted barycenter of all individual estimates with higher weights applied to more trusted agents. We show that such revisions naturally lead to an iterative algorithm which converges to a unique consensus estimate of the parameters. Furthermore, since the consensus estimate is itself a barycenter with computable weights, the group emerges as a collective super-agent with a well-formed opinion regarding the ability of each individual agent.

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Cite

BibTeXRIS
BibTeX
@misc{soklakov2026bregman,
  title = {{Bregman Consensus}},
  author = {Andrei N. Soklakov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35930},
  eprint = {2609.35930},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35930},
}
RIS
TY  - UNPB
TI  - Bregman Consensus
AU  - Andrei N. Soklakov
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35930
UR  - https://arxiv.org/abs/2609.35930
AB  - Consider a community of agents who are seeking consensus on a set of parameters. The agents agree to use the same Bregman-type divergence to quantify disagreement between their individual estimates of the parameters but have varying confidence in each other's abilities. Each agent is happy to revise their estimate by moving to the weighted barycenter of all individual estimates with higher weights applied to more trusted agents. We show that such revisions naturally lead to an iterative algorithm which converges to a unique consensus estimate of the parameters. Furthermore, since the consensus estimate is itself a barycenter with computable weights, the group emerges as a collective super-agent with a well-formed opinion regarding the ability of each individual agent.
ER  -