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On the Probability of Correct Selection in Ordinal Comparison over Dynamic Networks

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Abstract

We consider distributed ordinal comparison of selecting the best option which maximizes the average of local reward function values among available options in a dynamic network. Each node in the network knows only his reward function, and edge-connectivity across the nodes changes over time by Calafiore’s model. To estimate each option’s global reward function value, local samples for each option are generated at each node and those are iteratively mixed over the network by a weighted average of local estimates of instantaneous neighbors. Each node selects an option that achieves the maximum of the current global estimates as an estimate of the best option. We establish a lower bound on the probability of correct local-selection at any node, which uniformly converges over the nodes to a lower bound on the probability of correct global-selection by a virtual centralized node with the total available samples.

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Acknowledgements

The work of H.S. Chang was supported by the Sogang University Research Grant of 2009 (200811037). The work of J. Hu was supported in part by the Air Force Office of Scientific Research under Grant FA95501010340, and by the National Science Foundation under Grants CMMI-0900332 and CMMI-1130761.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Sogang University, Seoul, 121-742, Korea

    Hyeong Soo Chang

  2. Department of Applied Mathematics & Statistics, SUNY, Stony Brook, USA

    Jiaqiao Hu

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  1. Hyeong Soo Chang
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  2. Jiaqiao Hu
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Correspondence to Hyeong Soo Chang.

Additional information

Communicated by Qianchuan Zhao.

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Chang, H.S., Hu, J. On the Probability of Correct Selection in Ordinal Comparison over Dynamic Networks. J Optim Theory Appl 155, 594–604 (2012). https://doi.org/10.1007/s10957-012-0082-x

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  • DOI: https://doi.org/10.1007/s10957-012-0082-x

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