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Distributed Bregman-Distance Algorithms for Min-Max Optimization

  • Chapter
Agent-Based Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 456))

Abstract

We consider a min-max optimization problem over a time-varying network of computational agents, where each agent in the network has its local convex cost function which is a private knowledge of the agent. The agents want to jointly minimize the maximum cost incurred by any agent in the network, while maintaining the privacy of their objective functions. To solve the problem, we consider subgradient algorithms where each agent computes its own estimates of an optimal point based on its own cost function, and it communicates these estimates to its neighbors in the network. The algorithms employ techniques from convex optimization, stochastic approximation and averaging protocols (typically used to ensure a proper information diffusion over a network), which allow time-varying network structure. We discuss two algorithms, one based on exact-penalty approach and the other based on primal-dual Lagrangian approach, where both approaches utilize Bregman-distance functions.We establish convergence of the algorithms (with probability one) for a diminishing step-size, and demonstrate the applicability of the algorithms by considering a power allocation problem in a cellular network.

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Authors and Affiliations

  1. University of Illinois, Urbana, IL, 61801, USA

    Kunal Srivastava, Angelia Nedić & Dušan Stipanović

Authors
  1. Kunal Srivastava
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  2. Angelia Nedić
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  3. Dušan Stipanović
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Corresponding author

Correspondence to Kunal Srivastava .

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Editors and Affiliations

  1. Gdynia Maritime University, Str. Morska 81-87, Gdynia, 81-225, Poland

    Ireneusz Czarnowski

  2. Gdynia Maritime University, Str. Morska 81-87, Gdynia, 81-225, Poland

    Piotr Jędrzejowicz

  3. , Polish Academy of Science, Systems Research Institute, Str. Newelska 6, Warszawa, 01-447, Poland

    Janusz Kacprzyk

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Srivastava, K., Nedić, A., Stipanović, D. (2013). Distributed Bregman-Distance Algorithms for Min-Max Optimization. In: Czarnowski, I., Jędrzejowicz, P., Kacprzyk, J. (eds) Agent-Based Optimization. Studies in Computational Intelligence, vol 456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34097-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-34097-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34096-3

  • Online ISBN: 978-3-642-34097-0

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