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Randomized difference-based gradient-free algorithm for distributed resource allocation

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Abstract

This paper considers a distributed resource allocation problem over time-varying networks. The objective of each agent in the network is to optimize the sum of separable convex functions subjected to resource constraints by observing its local objective function and the information exchanged with its adjacent neighbors. Thus, the problem lies in a distributed framework. In existing literature dealing with similar problems, the measurement of the gradients/subgradients of the objective functions has been applied in the algorithm design. In this paper, by adding stochastic dithers to the local objective functions and constructing randomized differences, we propose a distributed gradient-free algorithm for solving the problem, and show that the algorithm is strongly convergent; that is, the estimates generated from each agent almost certainly converge to the optimal resource allocation solution of the network. Finally, the effectiveness of the algorithm is validated by conducting numerical experiments.

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Acknowledgements

This work was supported in part by National Key Research and Development Program of China (Grant No. 2018YFA0703800) and National Natural Science Foundation of China (Grant No. 61822312).

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoxue Geng & Wenxiao Zhao

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiaoxue Geng & Wenxiao Zhao

Authors
  1. Xiaoxue Geng
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  2. Wenxiao Zhao
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Correspondence to Wenxiao Zhao.

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Geng, X., Zhao, W. Randomized difference-based gradient-free algorithm for distributed resource allocation. Sci. China Inf. Sci. 65, 142205 (2022). https://doi.org/10.1007/s11432-020-3147-2

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  • DOI: https://doi.org/10.1007/s11432-020-3147-2

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